perfect and imperfect market essay

Perfect Markets in General Essay

Perfect market is a situational market that is rare in real life (Rittenberg & Tregarthen, 2011). Perfect competition in the market occurs in a way that it is difficult for any stakeholder to influence the price of commodities. In this case, automobile, beer and corn markets are examples of perfect market models.

A perfect competition market is, therefore, an imaginary situation that is characterized by large number of buyers and sellers. The buyers and sellers are many, but their individual consumer behavior has no impact on the market (Rittenberg & Tregarthen, 2011).

Similarly, the demand of one buyer is so insignificant compared to the total demand in the market and, therefore, no individual behavior can influence the prices. There are few competitive perfect markets in existence where the conditions of the perfect market are strict. (Salemi, & Hansen, 2005, p.29)

In this case, the automobile, beer and corn industries have influenced the buyer selection in their products so that products can be bought at different prices. A good example of perfect competitive market is where many farmers are producing corn.

Moreover, in the automobile industry, many dealers sell similar models of cars that one can barely differentiate. “The firms in these markets are price takers and are characterized by perfect knowledge, freedom of entry and exit of the market” (Salemi, & Hansen, 2005, p.29). There is also non-governmental interference in their activities, lack of excess supply and demand, and less transport costs.

In the beer and automobile industries, the seller has perfect knowledge about the market. Therefore, no one would conduct business at their preferred price other than the equilibrium price. For example, today a person could be assembling cars and then he or she can decide to clear the stock and start something else.

In these market models, all buyers are identical in the eyes of sellers. There are also no advantages of selling products to particular buyers (Salemi, & Hansen, 2005). The beer and the automobile companies have no personal recognition or preference of their buyers.

The prices in these markets are determined strictly by the interplay demand and supply. There is no government intervention in the form of taxes or subsidies, quotas, price controls among other regulations (Salemi, & Hansen, 2005). This factor makes the automobile and beer industries sell all what they supply in the market.

The buyers are able to buy all what they require because there is no deficit in supply. The other conditions that place these products under perfect mobility are factors of production. All factors of production including land, capital, labor, and entrepreneurship can be easily switched from one use to another. In beer, automobile, and corn market, factors of production are assumed to be perfectly mobile.

Further, it is assumed that buyers and sellers are located in one area. As such, they do not incur any costs in transporting their goods. The sellers in these markets cannot, therefore, charge higher prices to cover the cost of transport.

In the perfect markets, the buyers have perfect knowledge of the prices offered by different firms on certain products. The products sold have homogeneity. Perfect competition is advantageous to the society because the price equals the marginal cost of production in each firm. The price offered is reasonable and no single firm monopolizes the market.

Rittenberg, L., & Tregarthen, T. (2011). Principles of economics . Irvington, NY: Flat World Knowledge.

Salemi, M. K., & Hansen, W. L. (2005). Discussing economics: A classroom guide to preparing discussion questions and leading discussion . Cheltenham: Edward Elgar.

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Bibliography

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What Are Imperfect Markets? Definition, Types, and Consequences

Investopedia / Mira Norian

What Is an Imperfect Market?

An imperfect market refers to any economic market that does not meet the rigorous standards of the hypothetical perfectly—or purely—competitive market. Pure or perfect competition is an abstract, theoretical market structure in which a series of criteria are met. Since all real markets exist outside of the spectrum of the perfect competition model, all real markets can be classified as imperfect markets.

In an imperfect market , individual buyers and sellers can influence prices and production, there is no full disclosure of information about products and prices, and there are high barriers to entry or exit in the market.

A perfect market is characterized by perfect competition, market equilibrium, and an unlimited number of buyers and sellers.

Key Takeaways

• Imperfect markets do not meet the rigorous standards of a hypothetical perfectly or purely competitive market.
• Imperfect markets are characterized by having competition for market share, high barriers to entry and exit, different products and services, and a small number of buyers and sellers.
• Perfect markets are theoretical and cannot exist in the real world; all real-world markets are imperfect markets.
• Market structures that are categorized as imperfect include monopolies, oligopolies, monopolistic competition, monopsonies, and oligopsonies.

Understanding Imperfect Markets

All real-world markets are imperfect. Thus, the study of real markets is always influenced by competition for market share, high barriers to entry and exit, different products and services, prices set by price makers rather than by supply and demand, imperfect or incomplete information about products and prices, and a small number of buyers and sellers.

For example, traders in the financial market do not possess perfect or even identical knowledge about financial products. The traders and assets in a financial market are not perfectly homogeneous. New information is not instantaneously transmitted, and there is a limited velocity of reactions.

When considering the implication of economic activity, economists only use perfect competition models. A such, the term imperfect market is somewhat misleading. Most people will assume an imperfect market is deeply flawed or undesirable. However, this is not always the case. The range of market imperfections is as wide as the range of all real-world markets—some are much or less efficient than others.

Consequences of Imperfect Markets

Not all market imperfections are harmless or natural. Situations can arise in which too few sellers control too much of a single market, or when prices fail to adequately adjust to material changes in market conditions. It is from these instances that the majority of economic debate originates.

Some economists argue that any deviation from perfect competition models justifies government intervention, in order to promote increased efficiency in production or distribution. Such interventions may come in the form of monetary policy , fiscal policy, or market regulation. One common example of such interventionism is anti-trust law, which is explicitly derived from perfect competition theory.

Governments may also use taxation, quotas, licenses, and tariffs to help regulate so-called perfect markets.

Other economists argue that government intervention may not always be necessary to correct imperfect markets. This is because government policy is also imperfect, and government actors may not possess the right incentives or information to interfere correctly. Finally, many economists argue government intervention is rarely, if ever, justified in markets. The Austrian and Chicago schools notably blame many market imperfections on erroneous government intervention.

Types of Imperfect Markets

When at least one condition of a perfect market is not met, it can lead to an imperfect market. Every industry has some form of imperfection. Imperfect competition can be found in the following structures:

This is a structure in which there is only one (dominant) seller. Products offered by this entity have no substitutes. These markets have high barriers to entry and a single seller who sets the prices on goods and services. Prices can change without notice to consumers.

This structure has many buyers but few sellers. These few players in the market may bar others from entering. They may set prices together or, in the case of a cartel, only one takes the lead to determine the price for goods and services while the others follow.

Monopolistic Competition

In monopolistic competition, there are many sellers who offer similar products that can't be substituted. Businesses compete with one another and are price makers, but their individual decisions do not affect the other.

Monopsony and Oligopsony

These structures have many sellers, but few buyers. In both cases, the buyer is the one who manipulates market prices by playing firms against one another.

Imperfect Markets vs. Perfect Markets

Perfect markets are characterized by having the following:

• An unlimited number of buyers and sellers.
• Identical or substitutable products.
• No barriers to entry or exit.
• Buyers have complete information on products and prices.
• Companies are price takers meaning have no power to set prices.

In reality, no market can ever have an unlimited number of buyers and sellers. Economic goods in every market are heterogeneous, not homogeneous, as long as more than one producer exists. A diverse range of goods and tastes are preferred in an imperfect market.

Perfect markets, though impossible to achieve, are useful because they help us think through the logic of prices and economic incentives. It is a mistake, however, to try extrapolating the rules of perfect competition into a real-world scenario. Logical problems arise from the start, especially the fact that it is impossible for any purely competitive industry to conceivably attain a state of equilibrium from any other position. Perfect competition can thus only be theoretically assumed—it can never be dynamically reached.

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• Key Differences

Know the Differences & Comparisons

Difference Between Perfect Competition and Imperfect Competition

The type of market structure decides the market share of a firm in the market. If there exists a single firm, it will serve the entire market, and the demand of the customers are satisfied with that firm only. But if we increase the number of firms to two, the market will also be shared by the two. Similarly, if there are about 100 small firms in the market, the market is shared by all of them in proportion.

Therefore, it is the market structure, which affects the market. So here we are going to describe the differences between perfect competition and imperfect competition, in economics.

Content: Perfect Competition Vs Imperfect Competition

Comparison chart, definition of perfect competition.

Perfect Competition is an economic structure where the degree of competition between the firm is at its peak. Given are the salient features of the perfect competition:

• Many buyers and sellers.
• Product offered is identical in all respects.
• Any firm can come and go, as per its own discretion.
• Both the parties to the transaction are having complete knowledge about the product, quantity, price, market and market conditions as well.
• Transportation and Advertising cost is nil.
• Free from government interference.
• The price for a product is uniform across the market. It decided by the demand and supply forces; no firm can affect the prices, that’s why the firms are price takers.
• Each firm earns a normal profit.

Example : Suppose you go to a vegetable market to buy tomatoes. There are many tomato vendors and buyers. You go to a vendor and inquire about the cost of 1 kg tomatoes, the vendor replies, it will cost Rs. 10. Then you go ahead and inquire some more vendors. The prices of all the vendors are same for the demanded quantity. This is an example of perfect competition.

Definition of Imperfect Competition

The competition, which does not satisfy one or the other condition, attached to the perfect competition is imperfect competition. Under this type of competition, the firms can easily influence the price of a product in the market and reap surplus profits.

In the real world, it is hard to find perfect competition in any industry, but there are so many industries like telecommunications, automobiles, soaps, cosmetics, detergents, cold drinks and technology, where you can find imperfect competition . By the virtue of this, imperfect competition is also considered as real world competition.

There are various forms of imperfect competition, described below:

• Monopoly : Single seller dominates the entire market.
• Duopoly : Two sellers share the whole market.
• Oligopoly : Few sellers are there who either act in collusion or competition.
• Monopsony : Many sellers and a single buyer.
• Oligopsony : Many sellers and few buyers.
• Monopolistic Competition : Numerous sellers offering unique products.

Key Differences Between Perfect Competition and Imperfect Competition

The main points of difference between perfect competition and imperfect competition in economics are depicted below:

• The competitive market, in which there are a large number of buyers and sellers, and the sellers supply identical products to the buyers; it is known as perfect competition. Imperfect competition occurs when one or more conditions of the perfect competition are not met.
• Perfect competition is a hypothetical situation, which does not apply in the real world. Conversely, Imperfect Competition is a situation that is found in the present day world.
• When it comes to perfect competition, there are many players in the market, but in imperfect competition, there can be few to many players, depending upon the type of market structure.
• In perfect competition, the sellers produce or supply identical products. As against, in imperfect competition the products offered by the sellers can either be homogeneous or differentiated.
• If we talk about perfect competition, there are no barriers to the entry and exit of the firms which is just opposite in the case of imperfect competition.
• In perfect competition, it is assumed that the firms do not influence the price of a product. Hence they are price takers but in imperfect competition, the firms are price makers.

Perfect competition is an imaginary situation which does not exist in reality, but imperfect competition is factual i.e. which genuinely exist.

Whichever market, you consider for this like for example if you consider the detergent market. There are many players like Tide, Rin, Surf Excel, Ariel, Ghadi, etc. producing similar product i.e. detergent.

At first instance, you may think that this is an example of perfect competition, but this is not so. If you dig a little deeper, you may find that all the products are different as well as they vary in their prices. Some are low budget detergents for capturing the market of price sensitive people while others are high budget detergents for quality sensitive people.

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Junior Johnson says

February 16, 2022 at 2:08 am

Thanks much, am appreciating your lecture, very impressive God bless You 🙏🙏

Archana kumai says

October 12, 2022 at 9:41 pm

Thank you so much 🤗 for your helpful notes ☺️

March 28, 2022 at 10:32 pm

that was quiet amazing to explain my learners

khalphina says

August 3, 2023 at 4:25 pm

it is simple and good explanation

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Microeconomics

Course: microeconomics   >   unit 7.

• Introduction to perfect competition
• Perfect competition and why it matters
• Economic profit for firms in perfectly competitive markets
• How perfectly competitive firms make output decisions

Efficiency in perfectly competitive markets

• Perfect competition foundational concepts
• Long-run economic profit for perfectly competitive firms
• Long-run supply curve in constant cost perfectly competitive markets
• Long run supply when industry costs aren't constant
• Free response question (FRQ) on perfect competition
• Perfect competition in the short run and long run
• Increasing, decreasing, and constant cost industries
• Efficiency and perfect competition
• Long-run equilibrium in perfectly competitive markets meets two important conditions: allocative efficiency and productive efficiency.
• These two conditions have important implications. First, resources are allocated to their best alternative use. Second, they provide the maximum satisfaction attainable by society.

Self-check questions

Review questions.

• Will a perfectly competitive market display productive efficiency? Why or why not?
• Will a perfectly competitive market display allocative efficiency? Why or why not?

Critical-thinking questions

• Assuming that the market for cigarettes is in perfect competition, what do allocative and productive efficiency imply in this case? What do they not imply?
• In the argument for why perfect competition is allocatively efficient, the price that people are willing to pay represents the gains to society and the marginal cost to the firm represents the costs to society. Can you think of some social costs or issues that are not included in the marginal cost to the firm? Or some social gains that are not included in what people pay for a good?

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8 Debates on Perfect and Imperfect Competition

• Published: March 2016
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The chapter begins by considering various alternative views of competition: Smith, Ricardo, and Marx, who emphasize the antagonistic nature of capitalism and the turbulent character of competitive outcomes; Schumpeter and the Austrians, who treat competition as a process but retain some key neoclassical features; Marxian Monopoly Capital, Imperfect Competition, Kaleckian, and post-Keynesian schools, all of which rely on some version of imperfect competition; and modern Sraffian and classical traditions, which turn back to competition. The second section summarizes the contrasting patterns expected by various schools and compares them to the empirical evidence on pricing behavior, concentration, monopoly power, the ‘structure-performance’ findings from Bain, and the empirical results from Mann, Stigler, Brozen, Demsetz, and Semmler, among others. The evidence is shown to be quite consistent with the notion of real competition.

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Characteristics Of Perfect And Imperfect Markets

Market is a place where the buyers and sellers make transactions regarding goods and services. Depending on time, competition and extent of area, markets are classified into several types. On the basis of competition markets are classified into perfect markets and imperfect markets.

Perfectly competitive Markets:

Perfectly competitive market is one which consists of large number of buyers and sellers, uniform price and homogeneous commodities. No single buyer or seller is able to exercise control over the price of a commodity. The price of a commodity is same throughout the market. The following are the characteristics of perfect markets or perfectly competitive markets.

Characteristics of perfect markets:

1) There exists a large number of buyers and sellers. Each buyer buys a main portion of the whole stock of commodities. Similarity each seller sells a negligible portion of the whole stock of commodities. They have no influence over the determination of the price.

2) There prevails homogeneous commodities. The quantity and quality of commodities available in the market are the same. No differences are observed in the size, quality, taste of the Commodities.

3) Both the buyers and sellers will know the prices prevalent in the market. Neither of them can increase or decrease the price of a commodity. So the price line of a perfectly competitive market runs parallel to OX axis.

4) There exists no obstacles for the firms to enter or leave the industry. New firms enter the industry when there are huge profits. Old firms leave the industry when there are huge losses.

5) There exists no transport costs. As a result the price of the commodity is same at any place in the market.

6) Factors of production are freely mobile. They move from one industry to the other until they get higher remunerative prices for their services.

Distinction between pure competition and perfect competition:

‘Pure’ competition is a word introduced by Prof. Chamberlain. Pure competition is said to prevail when there exists large number of buyers and sellers, homogeneous commodities and freedom of admission into and exit of firms from an industry. In addition to these features perfect competition includes perfect knowledge of prices, free mobility of factors of production, absence of transport costs and uniform price as its features.

Both pure and perfect competitions are the two ideal concepts which can’t be found in real world. What we observe in reality is the prevalence of imperfect competition.

Imperfect Competition:

Imperfect competition consists of the features which are opposite to perfect competition. It has some special features.

Characteristics of imperfect markets:

1) There exists a small number of sellers in ‘this market. This enables the sellers to charge the prices as they like.

2) The number of buyers is also small. But its does not mean that buyers are few. The buyers in this market system are divided into several groups. Each group buys goods and services from different sellers.

3) The commodities bought and sold in this market are heterogeneous. They differ in their size, quality, appearance, tastes and durability.

4) The sellers adopt product differentiation and price discrimination. They collect different prices for the same commodity from different buyers.

5) There exists transport costs and selling costs in this market.

6) The consumers may not know the prevailing prices of the commodities in the market.

7) The factors of production are not freely mobile.

8) There prevails different prices for the same commodity in the same region.

Thus, imperfect competition consists of the features which are quite opposite to the perfect competition.

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Understanding Perfect and Imperfect Competition

Alexandra L.

Checked : T. M. H. , Luis G.

Latest Update 20 Jan, 2024

12 min read

Table of content

Perfect competition

How does the perfect competition work, large, homogeneous markets, perfect information, no controls, transportation is cheap and efficient, example of a perfectly competitive market, do perfect competition models have disadvantages, imperfect competition.

Perfect competition is a thought of microeconomics that looks at a market system where market forces have a monopolistic control. As long as these forces are met, the market is said to be in perfect competition. But, there has been no market that clearly defines ideal competition. In the real world, getting forces that work in perfect control is not possible; hence, all markets are classified as imperfect. A perfect market is simply a standard that measures how practical and real-world markets operate.

In   microeconomics , the study of perfectly competitive and not perfectly competitive markets is paramount. The subject affects most of the aspects of a real market in the economy, including decision making, supply, demand, pricing, and many other variables as you may already know, microeconomics one of the two major branches of economics and deal with the study of decisions made by individuals and firms. We are all faced with choices in our daily life. When it comes to fulfilling personal needs, for instance, one must forego one thing to achieve the other. And as you will discover throughout this article, these decisions affect and are equally affected by the economy. We shall, therefore, be looking perfect and imperfect competition as principles of microeconomics.

Perfect competition is only theoretical. This means you will only read about a perfectly competitive market structure in books and texts, but you will never experience it in real life.

A market is said to be in perfect competition when:

• All the firms involved in the market sell an identical product. The product is said to be a ‘commodity’ or ‘homogeneous.’ Every player is aware of what they and others are giving to or getting from the market.
• The firms are price takers. Since they are selling the same product, they cannot influence the market price of their individual products.
• Market share does not influence the price. However, small or big a firm is, they share similar pricing with others. In any case, they are only price takers.
• Buyers have complete information. Perfect information means buyers already know the past, future, and present of the product being sold and what each firm is charging.
• There are entirely free resources for this information.
• There is no barrier to entry into or exit from the market.

In contrast to this, perfect competition is the imperfect competition where a market violates the abstract tenets of perfectly competitive environments. All markets exist beyond the boundaries of ideal competition; hence they are categorized as imperfect. The modern concept of imperfect vs. perfect competition comes from the Cambridge classical culture of post-classical economic thought.

As stated, completely perfect competition does not exist. However, markets like commodities, such as oil or wheat, are highly competitive and liquid. They are, therefore, the closes the world can get to perfectly competitive markets.

This market is considered an “ideal type” or a market that bears the comparison for real-market structures. Theoretically, perfect competition is the direct opposite of a monopoly. For the case of monopoly, there is only a single firm in charge of producing and supplying a product or service, and they can price it any way they want. The consumer has no alternative, and would-be competitors cannot enter the market.

In perfect competition, there is equilibrium between demand and supply. In other words, there are many buyers and sellers; hence the price is determined by these variables. Companies don’t reap much profit, but just enough to stay in business. Any attempt to gain excess profits will attract other firms in the market, driving profits even lower.

In a perfect competition setting, there is enough supply and demand. The sellers are mostly small companies, as opposed to large corporations that can control prices. The product has minimal differences in terms of capabilities, features, and prices. Hence, buyers cannot differentiate between the products by only looking at the physical appearance like size and color or intangible values like the brand. And because there is a large population of both buyers and suppliers, supply and demand remain fairly constant within the market. Also, a buyer has a chance to substitute specific products from one firm for another's easily.

People and firms make decide based on available information. And in this case, there is information about the ecosystem and competition in a market that creates a significant advantage. For example, when there is knowledge about component sourcing and supplier pricing, individual firms may grow faster. Information about patents and researcher plans can have companies in pharmaceutical and technology initiate strategies that beat their competition.

Such issues are not in a perfectly competitive market. This is because the information is equally and freely available. This means, every firm produces its goods and serves at precisely the same rate and using the same techniques as the other companies in the same market.

In many instances, governments play a significant role in market systems. They impose regulations and price controls that shield both suppliers and consumers. Hence, they can control how firms enter or exit the markets. For instance, there are laws governing how the pharmaceutical industry does its research, product, and sale of drums.

These rules call for hefty capital   investments, including employees such as legal advisors and quality assurance, as well as infrastructure like machinery. When the costs are put together, it becomes costly for a company to bring a drug on the market.

The technology industry, on the other hand, works with less oversight. This means starting a company in technology is much easier and cheaper, and doing so in the pharmaceutical industry.

In a perfectly competitive environment, these controls do not exist. There is no restriction on how firms enter and exit the market.

In perfect competition, there are no issues with transport. Companies do not pay a lot for transport. As such, they can reduce the production costs as well as cut back the delays on transportation.

A perfectly competitive market is theoretical. Hence, finding an excellent example of real-life is not easy. But there are variants in the society that may bring out something close to perfect competition.

Think of a farmers’ market. Here, you will find many small buyers and sellers. There is often very little difference between their products, prices, and what others are selling. There is even no difference in the branding and packaging of the products. Thus, if one farm goes out of business, it may not leave any impact on the average price of the markets.

Also, consider supermarkets. In many cases, they stock the aisles in the same way from a set of companies. They all sell the same products, with little to no difference, including packaging, branding, and pricing.

Consider also the market for unbranded products. They are only cheaper versions of well-known products, and there no added value. Hence they retail at the same prices with no major differences generally.

Technology has also created another category of perfectly competitive markets. For instance, you will find all types of e-commerce sites offering similar products. Mostly, it is all about what they are selling. The internet is free and largely available; entry and exit are easy.

From an idealistic point of view, the perfect competition offers the perfect framework for the market establishment. However, the market is full of flaws and disadvantages. For instance, there is a lack of innovation. Firms are motivated to create better products and set themselves apart as an incentive to gain a more significant market share. For in perfect competition, a firm can possess dominance, hence no need for playing smart.

Demand and supply draw for fixed profit margins. Hence, a firm cannot charge premiums for their products and services. In such an environment, it would be very difficult for a company like Apple Inc to survive. Their phones are pricier than the competition.

This section introduces the student to how monopolies form (and) barriers to entry, the impact of output and price on profit-maximization, and monopolistic competition.

Before we go further, let's step back a bit into the history of monopoly. In 1773, one firm, East India Company, was on the verge of a big fail. It was going through a hard time for financial difficulties. But the British Parliament came to save the failing company by introducing the Tea Act. The law continued taxing tea and made the East India Company the only recognized tea supplier to American colonies. This step gave them legal monopoly power. But by November the same year, Boston citizens couldn’t take anymore. They refused tea unloading, stating, “no taxation without representation.” To cut the story short, things did not go very well.

A similar situation happened on the eve of the American Civil War in 1860 with the U.S cotton industry. The South was considering receding from the Union; hence they hoped to leverage on Britain imported coffee. But cotton –merchants refused to export their cotton; hence failing what was termed as “The King Cotton” strategy in 1861. Britain opted to other sources, but this affected the confederacy’s gold supply.

What we learn here is that monopoly sellers often don’t see a threat to their positions in the market. But it is all about the attribute of imperfect competition markets.

As we have learned above, a perfect competition environment is where no firm has market power. They only respond to market prices and changes. A monopolistic market is the opposite, where there is no competition at all. There is only one producer on the market, and they are responsible for changing the prices as they want. The consumer has no choice but to accept what they are given.

It is, however, important for a monopoly on being concerned about how the consumers will purchase their products. However, a monopolist never has to worry about the actions of other firms. They are not price-takers, as we saw with perfect competition.

In imperfect competition, the market violates tenets of the perfect competition. In other words, it allows some firms to have a stronger command on the market than others. It is an economic market that ignores the standards of purely competitive markets.

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In this case, companies come up with different products and services. They set their own price, and each fight for market dominance. Apart from monopolies, they are also found oligopolies, monopolistic, monopsonies, and oligopsonies.

A single-priced monopoly is a situation where a company must charge the same price to all consumers. In this case, the company majorly relies on aggregate demand.

Consider Oakley, Ray-Ban, and Persol sunglass companies. They are all owned by Luxottica, an eyewear company based in Italy that makes about 70% of all brand eyewear. This means the company dominates the market. But it is not a single-price monopoly. This is major because it bears different brands targeting different consumers; hence, they practice a form of price discrimination. If the company sold only a single category of glasses, they would have to sell at the same price, even if they owned 100% of the market. If they decided to lower the price, it would have to be for all consumers, and that would have a huge impact on their revenue. In a monopoly, price reduction leads to losing revenue, and the more sales they make, the greater the loss.

One of the drawbacks of imperfect competition is government intervention. Well, this may not be a limitation per se, considering that government regulations can help correct monopoly. They set policies that increase the quantity. But as we may already know taxes and price floors negatively affects quantity, which they will not work here. A subsidy, on the other hand, would increase market surplus, but it would be very difficult to implement. Perhaps the only option for this situation would be the price ceiling. Thus it will be reasonably applicable in reducing the deadweight loss. The most important thing here is sustaining the market equilibrium while protecting the consumers and the firm.

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THE DYNAMICS OF PERFECT MARKETS GRADE 12 NOTES - ECONOMICS STUDY GUIDES

• Key concepts
• Review of production, costs and revenue
• Perfect competition
• The individual business and the industry
• Market structures
• Output, profit, losses and supply
• How to draw graphs to show various equilibrium positions
• Competition policies

A perfect market is characterised by perfect competition. The conditions that result in perfect competition include:

• Equal access to the technology required for production
• No barriers to entry or exit from the marketplace
• Accurate and available market information
• No participant with the power to set the market price
• According to equilibrium theory, a perfect market will reach an equilibrium where the quantity supplied equals the quantity demanded at the market price

6.1 Key concepts

These definitions will help you understand the meaning of key Economics concepts that are used in this study guide. Understand these concepts well.

Use mobile notes to help you learn these concepts. Instructions for making them are on page xiv in the introduction.

6.2 Review of production, costs and revenue

Production takes place in the short run and the long run

• Short run The short run is the period of production where only the variable factors of production can change. The time period is too short to permit the number of firms in the industry to change.
• Long run The long run is the period of production where all factors can change. The time is long enough for variable and fixed factors to change. It allows enough time for new firms to enter the industry and/or existing firms to exit.

Table 6.1: Review of production, costs and revenue It is important to review production, cost and revenue concepts covered in Grade 11. This is vitally important for the understanding of cost and revenue curves for the different market structures which you will study in this section. Summary of costs

• The difference between the total cost and variable cost is the fixed cost
• TVC curve starts from 0 and TC starts from the fixed cost curve on the Y- axis.
• The gap between the AC curve and the AVC curve gets smaller as output increases.
• The MC Curve will always cut the AC and AVC curves at their minimum points.

6.3 Perfect competition

Perfect competition occurs in a market structure with a large number of participants who have access to all required information about the market place and are all price-takers. Prices are determined by demand and supply. Examples of market structures demonstrating most conditions of a perfect competition include the stock exchange, the foreign exchange market, the central grain exchange, and agricultural produce markets. A perfect market is a market where no single buyer or seller has a noticeable influence on the price of a good. This gives a true reflection of the scarcity value of goods and services. 6.3.1 Characteristics/conditions of a perfect market Products must be homogenous (i.e. identical)

• Products must be identical. There should be no differences in style, design and quality.
• In this way products compete solely on the basis of price and can be purchased anywhere.

There should be a large number of buyers and sellers

• It should not be possible for one buyer or seller to influence the price.
• When there are many sellers the share of each seller in the market is so small that the seller cannot influence the price.
• Sellers are price takers, they accept the prevailing market price. If they increase prices above the market price, they will lose customers.

No preferential treatment/discrimination

• Collusion occurs when buyers and sellers make an agreement to limit competition. In a perfect market no collusion takes place.
• Buyers and sellers base their actions solely on price, homogenous products fetch the same price and therefore no preference is shown for buying from or selling to any particular person.

Free competition

• Buyers must be free to buy whatever they want from any firm and in any quantity.
• Sellers must be free to sell what, how much and where they wish.
• There should be no State interference and no price control.
• Buyers should not form groups to obtain lower prices, nor should sellers combine to enforce higher prices.

Efficient transport and communication

• Efficient transport ensures that products are made available everywhere.
• In this way changes in demand and supply in one part of the market will influence the price in the entire market.
• Efficient communication keeps buyers and sellers informed about market conditions.

All participants must have perfect knowledge of market conditions

• All buyers and sellers must be fully aware of what is happening in any part of the market.
• Technology has increased competition as information is easily obtained via the internet.

Free access to and from markets

• Producers may enter and leave a market with little interference.
• Entering and leaving a perfect market is easy as less capital is required and there are fewer legal restrictions.

The factors of production are completely mobile

• They can move freely between markets.

In reality there are few perfect markets, however there are some sectors such as mining (e.g. gold) and agriculture (e.g. maize) where many of the conditions are met. These sectors illustrate the way in which the market mechanism works.

6.4 The individual business and the industry

6.4.1 Determining the market price To determine the market price for a firm under perfect competition you need to draw two graphs next to each other. On the left is the graph for the industry and on the right is the graph for the firm (individual producer).

• Figure 6.2 a) (the industry) shows the interaction of demand and supply (market forces).
• The market forces are in equilibrium at the point of intersection of the demand and supply curves, at “e”.
• At equilibrium the quantity demanded is equal to the quantity supplied. This determines the market price.
• Now look at Figure 6.2 b) (firm or individual producer). One producer will not be able to influence the market price and has to accept the market price (P1), he is a price taker.
• Because this is the only price the producer can charge, the demand curve for the producer is a straight line drawn at price P1.
• This horizontal line at the market price (P1) is the demand curve (DD), the average revenue (AR) curve and the marginal revenue (MR) curve.

Read this section on graphs through five times, and redraw each graph each time. 6.4.2 Demand curve for an individual producer The individual producer is a price taker and sells goods at the market price. At this price, demand remains constant. A higher price such as P2 cannot be charged as customers will be lost to other producers. A lower price such as P3 cannot be charged as a small profit or a loss will be made.

• At all pionts where MR is above MC, the firm is adding to profit. From unit 1-3, the firm is increasing its profit.
• At all points where MC is above MR, the firm is decreasing profit. From unit 5-7, the firm’s profit will decrease.
• The firm maximises profit where MR = MC. The firm maximises its profits at unit 4.

Table 6.5: Depicting Profit Maximisation

• If TC > TR the business makes a loss. If TR > TC it makes a profit.
• Maximum profit is achieved at units 3 and 4.
• Once the maximum profit is achieved, profits start to decrease with the next unit of output.
• Therefore the firm will not produce more than 4 units.
• At all points where TR is above TC, the firm is making a profit.
• At all points where TC is above TR, the firm is making a loss.
• The gap between TR and TC represents profit.
• Profit is maximised when the gap between TR and TC is the greatest. This is occurs at between 3 and 4 units.

6.5 Market structures

There are FOUR different market structures:

• Monopolistic competition

Table 6.6 shows the 5 broad characteristics which distinguish the four market structures: As you study each market structure in detail, you will be able to identify more distinguishing characteristics.

6.6 Output, profit, losses and supply

• Given a market price of P3, profit is maximised where MR = MC = P 3.
• This occurs at a quantity of Q 3 .
• At Q 3 the firm’s average revenue (AR) per unit of production is P 3,
• The average cost per unit is C 1 which is lower than the price of P 3.
• The firm is making an economic profit per unit of production of P 3 – C 1.

Another explanation

• Total revenue equals P 3 × Q 3, therefore total revenue is represented by the area 0P 3 E 3 Q 3 .
• Total cost equals C 1 × Q 3, this is represented by the area 0C 1 MQ 3.
• The difference between these two areas is the economic profit which is represented by the light grey shaded area C 1 P 3 E 3 M.

When Average Revenue is above Average cost the firm makes an ECONOMIC PROFIT.

• Given a market price of P 3, profit is maximised where MR = MC at point E 3.
• This occurs at a quantity of Q 3.
• At Q3 the firm’s average revenue (AR) per unit of production is P 3,
• The average cost per unit is C 3 which is higher than the price of P 3.
• The firm is making an economic loss per unit of production which is equal to the difference between C 3 and P 3.

Another explanation.

• Total revenue equals P 3 × Q 3, therefore total revenue is represented by the area 0P 3 E 3 Q 3.
• Total cost equals C 3 × Q 3, this is represented by the area 0C 3 MQ 3.
• The difference between these two areas is the economic loss which is represented by the light grey shaded area C 3 P 3 E 3 M.
• Whether the firm should continue production would depend on the level of AR (that is P3) relative to the firm’s average variable cost.

3. Normal profits

• A firm makes normal profits when total revenue (TR) equals total costs or when average revenue (AR) equals average cost (AC).
• Normal profit is the maximum return the owner of a firm expects to receive to keep on operating in the industry.
• Given a market price of P 2, profit is maximised where MR = MC = P 2.
• This occurs at a quantity of Q 2.
• At Q2 the firm’s average revenue (AR) per unit of production is P2, which is also equal to the average cost per unit C 2 (AC).
• Since AR = AC, the firm earns a normal profit since all its costs are fully covered.
• Point E 2 is usually called the break-even point.
• Total revenue equals P2 x Q2, therefore total revenue is represented by the area 0P2E2Q2.
• Total cost equals C2 × Q2, this is represented by the area 0P2E2Q2.
• Since Total revenue equals Total Cost the producer makes a normal profit.

The individual business can make an economic profit, economic loss or normal profit in the Short Run. They are referred to as short run equilibrium positions. In the long run the individual business will always make normal profit. 6.6.2 The industry The long term equilibrium for the industry and the individual firm The impact of entry and exit on the equilibrium of the firm and industry

• Profits are a signal for the entry of new businesses.
• Losses are a signal for businesses to leave the market.
• The long-term equilibrium in the perfect market will be influenced by the entry or exit of individual businesses.
• If individual farmers are earning an economic profit at P 1.
• New farmers will enter the market, more apples will be supplied.
• The market supply curve will shift to the right from S 1 to S 2.
• The Equilibrium price will drop from P 1 to P 2.
• Individual farmers will then earn normal profits. There will be no further reason for new farmers to enter the market. The industry is in equilibrium.
• If individual farmers are making economic losses, some farmers may leave the industry.
• When a few farmers leave the market, fewer apples will be supplied.
• The market supply curve will shift to the left from S 1 S 1 to S 2 S 2.
• The equilibrium price will increase from P 1 to P 2. Individual farmers will then earn normal profits. There will be no reason for individual farmers to leave the market.
• Therefore in a perfect market the long term equilibrium is achieved when individual firms earn a normal profit.
• Point a: a firm will not produce here because AR < AVC
• Point b: it is the lowest price that the firm will charge (shut-down point). It represents the beginning of the supply curve.
• Point c: the firm is making an economic loss. Because AR < AC. The loss is minimised because the firm produces where MR = MC.
• Point d: the firm is making normal profit (breaking even) because AR = AC.
• Point e: the firm is making economic (supernormal) profits because AR > AC.

6.7 How to draw graphs to show various equilibrium positions

First draw your TWO axes: Price (P) on the vertical axis and Quantity (Q) on the horizontal axis. Remember, they meet at the origin (0). Note that the labelling of the axes is not the same for all graphs. In showing the various equilibrium positions the following sequence should be followed.

• Draw the demand curve followed by the Marginal revenue curve, (in a perfect market D = MR = AR).
• Then draw the AC curve.
• Then draw the MC curve which must cut the AC curve at its minimum point.
• Identify profit maximising point. MC = MR
• Determine quantity (drop a line from the profit maximizing point to the x-axis).
• Determine price (extend line upwards from the profit maximizing point to the demand curve) and then extend the line horizontal to the y-axis.
• Compare AR/price to AC to determine profit or loss.

Everything is important – do not leave out anything! Each step counts for marks. Label all axes, curves and graphs. Note the following:

• To show economic profit the AC curve must cut the demand curve.
• To show normal profit the minimum point on AC curve must be at a tangent to the demand curve.
• To show economic loss the AC curve must not touch demand curve.

6.8 Competition policies

6.8.1 Description Competition refers to the existence of free entry into and exit from markets. This ensures that markets are not dominated by certain businesses. 6.8.2 Goals of competition policy

• To prevent monopolies and other powerful businesses from abusing their power.
• To regulate the formation of mergers and acquisitions who wish to exercise market power.
• To stop firms from using restrictive practices like fixing prices, dividing markets etc.

6.8.3 The Competition Act in South Africa The government introduced the Competition Act 89 of 1998 to promote competition in South Africa in order to achieve the following objectives:

• promote the efficiency of the economy (its primary aim)
• provide consumers with competitive prices and a variety of products
• promote employment
• encourage South Africa to participate in world markets and accept foreign competition in South Africa
• enable SMMEs to participate in the economy
• to allow the previously disadvantaged to increase their ownership of businesses
• Define the concept market structure. (2)
• How many sellers will one find in a monopoly market? (2)
• In what market are all participants price-takers? Motivate your answer. (4)
• Explain the shape of the individual demand curve under perfect competition. (4)
• Vodacom (6)
• Explain in your own words the message behind the pie-charts shown above. (4)

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An introduction to perfect and imperfect competition via bilateral oligopoly

• Open access
• Published: 20 January 2021
• Volume 133 , pages 103–128, ( 2021 )

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• Alex Dickson 1 &
• Simone Tonin   ORCID: orcid.org/0000-0001-9495-7265 2  

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A Correction to this article was published on 17 September 2022

This article has been updated

This paper explores the study of bilateral oligopoly, in which both sellers and buyers have substantial influence on the market. We lead readers coherently through the key results that emerge from the literature on bilateral oligopoly by means of worked examples based on the same underlying two commodity exchange economy, along with broader consideration of the relevant literature. This allows us to concisely compare the different equilibrium outcomes when agents act simultaneously vs sequentially, and when some/all agents are assumed to behave competitively, giving the reader much-needed straightforward access to the results of this challenging literature.

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1 Introduction

“It seems impossible to go on with analysing markets under the assumption of perfect competition. Direct observation of economic activity reveals that markets are the fields of “giants”, operating simultaneously with a fringe of small competitors. Even partial analysis has taken this picture of the market when proposing oligopoly solutions to describe the outcomes of imperfectly competitive markets. Behind the demand function there is a myriad of “small” price-taking agents, while the supply side is occupied by few agents appearing as giants, contrasting with the dwarfs on the demand side.” Gabszewicz ( 2013 )

The study of market power in imperfectly competitive markets has commanded much attention from economists. The workhorse model of industrial organization economists—that of Cournot competition—takes a partial equilibrium perspective and makes the assumption that only firms have market power. Bilateral oligopoly is a natural generalization of Cournot competition to consider markets in which both sellers and buyers can have market power and so behave strategically in manipulating prices to be more favourable to them. The purpose of this exposition is to introduce the reader to the study of bilateral oligopoly by leading them through non-trivial examples Footnote 1 that illustrate some of the main ideas to emerge from the literature. Furthermore, the examples provide a unified framework to compare different kinds of oligopoly: symmetric oligopoly, where all agents are permitted to act strategically; asymmetric oligopoly, where only some agents act strategically with the rest assumed to behave as price takers; simultaneous oligopoly, where sellers and buyers make their choices without knowledge of others’ decisions; and sequential oligopoly, where some agents move first.

Bilateral oligopoly was first introduced by Gabszewicz and Michel ( 1997 ). The model is that of an economy in which there are two commodities and agents have “corner endowments”, i.e., they are endowed with only one of these two commodities. In a noncooperative game, agents can then choose the amount of their initial endowment to put up in exchange for the other commodity. It is often convenient to think of the first of the two commodities as a consumption good and the second as commodity money (which can be viewed as a numeraire), in which case the agents endowed with the consumption good are called sellers, and those endowed with the commodity money are buyers. Despite the simplicity of the model, this structure is rich enough to study many interesting phenomena that may arise in imperfectly competitive economies. A fruitful line of research focuses on testing the robustness of the partial equilibrium analysis of Cournot oligopolies to general equilibrium models without production where all agents, sellers and buyers, have market power. For instance, Bloch and Ghosal ( 1997 ) and Bloch and Ferrer ( 2001a ) study agents’ incentives to create submarkets as the Cournot game suggests that firms could gain market power by forming smaller submarkets. Dickson and Hartley ( 2008 ) and Amir and Bloch ( 2009 ) focus on the existence of Nash equilibrium and the comparative static properties of the equilibrium. Dickson ( 2013a ) pays particular attention to the effect of entry of additional sellers in bilateral oligopoly, comparing the results to the conventional wisdom from the Cournot model, and Dickson and Hartley ( 2013a ) consider whether bilateral oligopoly and Cournot competition are equivalent when there are many buyers.

The bilateral oligopoly model belongs to the line of research on strategic market games initiated by the seminal papers of Shubik (1973), Shapley ( 1976 ), and Shapley and Shubik ( 1977 ). There are many types of strategic market games (see Giraud ( 2003 ) and Levando ( 2012 ) for a survey). Here we mention only the “trading post model” and the “window model” which can be seen as different institutional mechanisms through which prices are determined. In the first model, trade is decentralised through a system of trading posts where commodities are exchanged. Dubey and Shubik ( 1978 ) studied the trading post model where only commodity money is used to buy other commodities while Amir et al. ( 1990 ) considered the case in which any commodity can be used to buy other commodities. Footnote 2 Differently, Sahi and Yao ( 1989 ) studied the window model where trade is centralised by a clearing house in which there is a “window” for each commodity. This model was first proposed informally by Lloyd S. Shapley, and we call it the “Shapley window model”. It is important to stress that when there are only two commodities, as in bilateral oligopoly, all three models coincide.

We start our analysis by recasting the classical Cournot game as an exchange game where firms are replaced by sellers characterised by initial endowments and utility functions, and buyers are represented by a demand function. Next, we consider the Cournot-Walras equilibrium concept in exchange economies, introduced by Codognato and Gabszewicz ( 1991 ) and Gabszewicz and Michel ( 1997 ). This model describes, in a general equilibrium framework, the same kind of imperfect competition as the Cournot game in which the buyers are assumed to be price takers from whence a demand function can be derived. The exchange versions of these cornerstone models to study imperfect competition allow us to compare them with the bilateral oligopoly model in a clear way. In fact all examples in the paper are based on the same exchange economy where sellers have quasi–linear utility functions and buyers have quasi-linear quadratic utility functions that generate a linear demand which does not exhibit wealth effects (so long as wealth is large enough). By comparing the different approaches we find that there are two main differences between the Cournot-Walras approach and the bilateral oligopoly model.

First, bilateral oligopoly describes a symmetric oligopoly since all agents are allowed to act strategically in manipulating prices by changing their actions, whereas the Cournot-Walras approach describes an asymmetric oligopoly where only the sellers are allowed to act strategically while the buyers are assumed to treat prices as given and beyond their control.

Second, the Cournot-Walras approach has an intrinsic two-stage nature which cannot be reconciled with the Cournot-Nash equilibrium of simultaneous-move bilateral oligopoly where all agents act simultaneously. In order to capture the two-stage structure considered in Cournot-Walras, we define a sequential bilateral oligopoly, where sellers move in the first stage and buyers move in the second stage, and we adopt subgame-perfect Nash equilibrium as the equilibrium concept. As in bilateral oligopoly, all agents are treated symmetrically in this model, in the sense that no agents are assumed to be price takers.

The comparison between the Cournot-Walras approach and the bilateral oligopoly model raises the question of whether models that impose the behavioural assumption of price taking on some agents can be reconciled with fully strategic models. This is the so-called problem of the “foundations of oligopoly” which seeks to understand under which conditions price taking behaviour emerges endogenously, and therefore whether the assumption of price taking is appropriate. We deal with this question by replicating the economy to increase the number of buyers while leaving the number of sellers fixed (which we do by following the partial replica approach proposed by Dickson and Hartley ( 2013a ) which replicates the set of buyers while proportionally reducing their weight). As we do so, buyers lose their ability to influence prices and so behave more and more like price takers. We provide an example showing that, in the many-buyer limit, the equilibrium in a sequential version of bilateral oligopoly in which the sellers move first and the buyers move second coincides with the Cournot-Walras equilibrium (that has the same sequential nature but assumes price taking) so sequential bilateral oligopoly provides a foundation for the Cournot-Walras approach. In contrast, the equilibrium in the simultaneous version of bilateral oligopoly remains distinct from the Cournot-Walras equilibrium even in the many-buyer limit. As such, to provide a foundation for the Cournot(-Walras) equilibrium concept a large number of buyers is necessary but not sufficient: buyers must also move after sellers have irreversibly committed to their decisions.

In the last part of our paper, we study the relationship between the Walras (competitive) equilibrium and the other equilibrium concepts examined. To this end, we show an example where, when all agents in the economy are replicated as in Debreu and Scarf ( 1963 ), sellers’ and buyers’ commodity bundles at the limit of the Cournot-Nash equilibrium in simultaneous bilateral oligopoly correspond to the commodity bundles at the Walras equilibrium. This is not surprising because, as in the partial replica, when agents are replicated they lose market power and in the limit behave competitively. Since all agents are replicated, in the limit everyone behaves competitively and then the outcome must be Walrasian. Therefore, the bilateral oligopoly model can be used to study the foundations of perfect competition as price taking behaviours can be obtained endogenously in equilibrium when the number of all agents increases without bound. Footnote 3

We conclude our analysis by making some welfare comparisons of the different types of competition analysed. By the first welfare theorem, the Walras equilibrium is Pareto efficient while the allocations obtained with the other equilibrium concepts are Pareto inefficient. This can easily be seen because there exists an allocation that Pareto dominates the one obtained at any equilibrium different from the Walras equilibrium. In other words, when markets are imperfectly competitive the equilibrium outcome is Pareto inefficient.

The rest of the paper has the following structure. In Sect.  2 we introduce the Cournot exchange game. In Sect.  3 we describe the Cournot-Walras approach. In Sect.  4 after having defined the simultaneous bilateral oligopoly model and the Cournot-Nash equilibrium, we give an example with a finite number of agents and an example where we partially replicate the exchange economy concluding there may be differences between a simultaneous bilateral oligopoly and the Cournot-Walras approach even when the number of buyers is large. In Sect.  5 we introduce the sequential bilateral oligopoly model, we partially replicate the exchange economy, and we compare the limit of the subgame-perfect Nash equilibrium with the Cournot-Walras equilibrium. In Sect.  6 we compare our previous results with the Walras equilibrium and we make some welfare considerations. In Sect.  7 we draw some conclusions and we outline some open problems.

2 Cournot game (partial equilibrium analysis)

“Let us now imagine two proprietors and two springs of which the qualities are identical, and which, on account of their similar positions, supply the same market in competition.” A. A. Cournot (1838)

In this section, by taking a slightly different approach from the one proposed by Cournot ( 1838 ), we consider the two proprietors as sellers of water and not as producers. This means that they are characterised by an endowment of the good and utility functions instead of cost functions. Footnote 4 Note, however, that with a quasi-linear utility specification as we use in our examples, the two approaches are very similar as the disutility from not consuming the good when it is supplied to the market can be interpreted as a cost of supply. The consumption good (water in Cournot’s example) is denoted by x and it is exchanged for money which is denoted by y . Footnote 5 A commodity bundle ( x ,  y ) is a point in \(\mathbb {R}_+^2\) which is the set of all feasible commodity bundles. As in Cournot ( 1838 ), we assume that buyers are represented by the demand for the consumption good which is a downward sloping function of the price, i.e., \(D=f(p_x)\) . Each seller is characterized by a utility function, \(u_i:\mathbb {R}_+^2\rightarrow \mathbb {R}\) , which represents their preferences, and by an initial endowment, \((x_i^0,y_i^0)\in \mathbb {R}_+^2\) , such that \(x_i^0>0\) and \(y_i^0=0\) , i.e., sellers hold only the consumption good. Sellers face the demand and we assume that they choose a supply of the consumption good in order to obtain a commodity bundle which maximises their utility. We suppose that there are m sellers.

We now introduce the Cournot exchange game \(\Gamma\) . The strategy set of seller i is

with \(q_i\) the offer of the consumption good that seller i puts up in exchange for money. Let \(\mathcal {Q}=\prod _{i=1}^m\mathcal {Q}_i\) and \(\mathcal {Q}_{-h}=\prod _{i\ne h}\mathcal {Q}_i\) . Let \(\mathbf{q}=(q_1,\dots ,q_m)\) and \(\mathbf{q}_{-i}=(q_1,\dots ,q_{i-1},q_{i+1},\dots ,q_m)\) be elements of \(\mathcal {Q}\) and \(\mathcal {Q}_{-i}\) respectively. We denote by \(Q=\sum _{i=1}^mq_i\) the total amount of the consumption good offered for sale by sellers. Cournot’s model implicitly assumes there is an auctioneer who adjusts the price so that the market clears, that is, total supply equals the amount demanded. As such, for each \(\mathbf{q}\in \mathcal {Q}\) , the price of the consumption good is \(p_x(\mathbf{q})=f^{-1}(Q)\) which implies \(D=Q\) and \(p_y\) is normalized to 1. For each \(\mathbf{q}\in \mathcal {Q}\) , the commodity bundle \((x_i(\mathbf{q}),y_i(\mathbf{q}))\) of a seller i is given by

for \(i=1,\dots ,m\) . The payoff function of a seller i is

for \(i=1,\dots ,m\) . A Cournot exchange game is then a set \(\Gamma =\{(\mathcal {Q}_i,\pi _i(\cdot ))_{i=1}^m\}\) . We now introduce the definition of a Cournot equilibrium.

Definition 1

The strategy profile \(\hat{\mathbf{q}}\) is a Cournot equilibrium for the game \(\Gamma\) if for each seller \(i=1,\ldots ,m\) we have \(\pi _i(\hat{q}_i,\hat{\mathbf{q}}_{-i})\ge \pi _i(q_i,\hat{\mathbf{q}}_{-i})\) , for each \(q_i\in \mathcal Q_i\) .

We now consider an example to illustrate the Cournot equilibrium concept.

Consider a market with two sellers such that \(u_i(x,y)=\ln (1+x)+y\) and \((x_i^0,y_i^0)=(3,0)\) , for \(i=1,2\) . Buyers are represented by the demand function \(D=6-2p_x\) . Since we assume that the market for the consumption good clears, \(D=q_1+q_2\) , we obtain \(p_x(\mathbf{q})=3-\frac{1}{2}(q_1+q_2)\) . To find the Cournot equilibrium we need to find the strategies \(\hat{q}_1\) and \(\hat{q}_2\) which maximise the sellers’ payoffs. Consider, without loss of generality, the maximisation problem for seller 1

This payoff function is strictly concave in \(q_1\) , and an easy way to find the maximum is to solve the problem as an unconstrained maximisation problem then check the constraints are satisfied. The first-order condition is

Since sellers are identical, we consider the symmetric Cournot equilibrium where \(\hat{q}_1=\hat{q}_2\) , in which

(which, of course, satisfies the constraints). At the Cournot equilibrium the price is \(p_x(\hat{\mathbf{q}})=\frac{\sqrt{15}}{3}\) , demand for the consumption good is \(D=\frac{18-2\sqrt{15}}{3}\) and the sellers’ commodity bundles are

\(\square\)

While we consider a slight variation on the original Cournot model as we treat firms as sellers with utility functions, the underlying principles are exactly the same. Shubik (1973) raised the following critique to this type of oligopoly model:

“The Cournot duopoly model is an open market model involving money. After trade has taken place neither the amount of goods nor the amount of money in the system is conserved. Goods flow out into the market and money flows in from the market.”

Shubik’s paper advocates a closed market model, where commodities flow within the system and after trade the total amount of each commodity does not change. In our example due to our treatment of the sellers the amount of the consumption good is preserved, but it is immediate to see that the final amount of money is coming from outside the model. This is a typical feature of partial equilibrium models where each market is considered in isolation from the rest of the economy. Therefore, M. Shubik is suggesting to study oligopoly within a general equilibrium model. Furthermore, another critical feature of the Cournot exchange game is that agents are modelled in different ways: sellers are represented by utility functions and initial endowments while buyers are represented by a demand function. Footnote 6

In the next section we address these two issues by introducing a two-commodity exchange economy with corner initial endowments and by using the Cournot-Walras equilibrium as solution concept.

3 Cournot-Walras approach

We start by defining the buyers who have been represented by a demand function in the previous model. A buyer is characterised by a utility function \(u_i:\mathbb {R}_+^2\rightarrow \mathbb {R}\) which represents their preferences and by an initial endowment, \((x_i^0,y_i^0)\in \mathbb {R}_+^2\) , such that \(x_i^0=0\) and \(y_i^0>0\) , i.e., buyers hold only money. We suppose that there are n buyers in the exchange economy indexed \(i=m+1,\ldots ,m+n\) . The difference between sellers and buyers in this model lies in the initial endowments: sellers hold only the consumption good while buyers hold only money (the availability of which is therefore fixed at their total endowment). We can now formally define an exchange economy \(\mathcal {E}=\{(u_i(\cdot ),(x_i^0,y_i^0))_{i=1}^{m+n}\}\) which is the set containing all the pairs \((u_i(\cdot ),(x_i^0,y_i^0))\) describing sellers and buyers. In two-commodity exchange economies the price vector is simply \(\mathbf{p}=(p_x,p_y)\) .

We now describe the agents’ behaviours in the Cournot-Walras approach. In the Cournot game sellers were permitted to act strategically while buyers’ behaviour was not modelled but represented by a demand function. The Cournot-Walras approach derives the Walrasian (competitive) demands of the buyers from their characteristics making the explicit assumption that they are price takers. The Walrasian demands of a buyer i are the functions \(x_i(\mathbf{p})\) and \(y_i(\mathbf{p})\) that associate to each positive price vector an amount of commodity x and y that maximises the utility function \(u_i(\cdot )\) in i ’s budget set \(\{(x,y)\in \mathbb {R}_+^2: p_xx+p_yy\le p_yy_i^0\}\) . Footnote 7 In other words, for any positive price vector \(\mathbf{p}\) , the amounts \(x_i(\mathbf{p})\) and \(y_i(\mathbf{p})\) solve the following maximisation problem Footnote 8

for any buyer i . We assume again that the market of each commodity clears. Therefore, for each \(\mathbf{q}\in \mathcal {Q}\) , the price vector \(\mathbf{p}\) at a Cournot-Walras equilibrium must solve

i.e., buyers’ total demand of the consumption good must be equal to sellers’ total supply of the consumption good. We denote by \(\mathbf{p}(\mathbf{q})\) the price vector \((p_x(\mathbf{q}),1)\) that solves equation ( 5 ). Footnote 9 If equation ( 5 ) holds then the market for money also clears. By having described the price formation rule, which is purely Walrasian, we can now define the rules to calculate the commodity bundle of each agent. The buyers’ commodity bundles are given by the Walrasian demands calculated at the price vector \(\mathbf{p}(\mathbf{q})\) . Since sellers’ strategies are the same as in the Cournot exchange game, their commodity bundles are given according to the equations in ( 2 ) at the price vector \(\mathbf{p}(\mathbf{q})\) . Consequently sellers’ payoff functions are defined as in ( 3 ). We finally introduce the notion of an allocation \((x_i,y_i)_{i=1}^{n+m}\) which is a specification of a commodity bundle for each seller and buyer.

We now have all the elements to define the Cournot-Walras equilibrium for the exchange economy \(\mathcal {E}\) .

Definition 2

A Cournot-Walras equilibrium for the exchange economy \(\mathcal {E}\) is a vector \(\tilde{\mathbf{q}}\) and an allocation \((\tilde{x}_i,\tilde{y}_i)_{i=1}^{n+m}\) such that

for each seller \(i=1,\ldots ,m\) we have \(u_i(x_i(\tilde{q}_i,\tilde{\mathbf{q}}_{-i}),y_i(\tilde{q}_i,\tilde{\mathbf{q}}_{-i}))\ge u_i(x_i(q_i,\tilde{\mathbf{q}}_{-i}),y_i(q_i,\tilde{\mathbf{q}}_{-i}))\) , for each \(q_i\in \mathcal Q_i\) ;

\((\tilde{x}_i,\tilde{y}_i)=(x_i(\tilde{\mathbf{q}}),y_i(\tilde{\mathbf{q}}))\) for the sellers \(i=1,\dots ,m\) and \((\tilde{x}_i,\tilde{y}_i)=(x_i(\mathbf{p}(\tilde{\mathbf{q}})),y_i(\mathbf{p}(\tilde{\mathbf{q}})))\) for the buyers \(i=m+1,\dots ,n\) .

We now consider an example to illustrate the Cournot-Walras equilibrium concept.

Consider an exchange economy with 2 sellers and 2 buyers such that \(u_i(x,y)=\ln (1+x)+y\) and \((x_i^0,y_i^0)=(3,0)\) , for \(i=1,2\) (the sellers), and \(u_i(x,y)=3x-\frac{1}{2}x^2+y\) and \((x_i^0,y_i^0)=(0,5)\) , for \(i=3,4\) (the buyers). Footnote 10 To calculate a Cournot-Walras equilibrium, the first step is to find buyers’ Walrasian demands. The constrained maximisation problem the buyers face is

By using the Lagrange multiplier method, we can obtain the Walrasian demands

for \(i=3,4\) . Study of the second-order conditions reveals the solution corresponds to a maximum. Footnote 11 Since we normalise \(p_y=1\) , the price of the consumption good which solves equation ( 5 ) is

By construction, this is the same inverse demand function as in Example 1, but derived from buyers’ characteristics rather than assumed. Therefore, it is immediate to see that each seller’s maximisation problem is equivalent to that in ( 4 ) from Example 1, so \((\tilde{q}_1,\tilde{q}_2)=(\frac{9-\sqrt{15}}{3},\frac{9-\sqrt{15}}{3})\) and \(\mathbf{p}(\tilde{\mathbf{q}})=(\frac{\sqrt{15}}{3},1)\) . Finally, the allocation at the Cournot-Walras equilibrium is

It is immediate to see that sellers’ commodity bundles and the total demand of the consumption good from buyers correspond to the ones at the Cournot equilibrium. Therefore, the Cournot-Walras equilibrium captures, in a general equilibrium framework, the same kind of competition as the Cournot exchange game but where the total quantities of the two commodities in the system are preserved, and buyers’ behaviour is explicitly modelled, assuming they are price takers. In other words, the Cournot-Walras approach allows us to study asymmetric oligopoly in a general equilibrium setting, with sellers acting strategically and buyers assumed to treat prices as fixed. Therefore, oligopoly models based on exchange economies can address Shubik (1973)’s critique.

The Cournot-Walras equilibrium concept was introduced by Gabszewicz and Vial ( 1972 ) in a production economy and it was recast in exchange economies by Codognato and Gabszewicz ( 1991 ) and subsequently by Gabszewicz and Michel ( 1997 ). These contributions consider exchange economies characterised by few oligopolists (sellers in our case) and many small agents (buyers in our case). In the Cournotian spirit, the oligopolists are allowed to act strategically as they are few, while small agents are assumed to act competitively as price takers as they are many. However this kind of assumption was criticised by Okuno et al. ( 1980 ):

“Traditional general equilibrium treatments of such situations [in which some but not all agents have market power] have been deficient in that they have simply assumed a priori that certain agents behave as price takers while others act non-competitively, with no formal explanation being given as to why a particular agent should behave one way or the other.”

Our Example 2 supports this view as it shows that it is possible to use the Cournot-Walras equilibrium in odd cases where buyers are assumed to behave competitively even if there are only two of them. In other words, the Cournot-Walras approach does not endogenously derive agents’ behaviours but it assumes a priori that some agents can influence prices while others are price takers. Footnote 12

The issue of asymmetrically imposing behavioural assumptions on some agents is overcome in bilateral oligopoly models in which both sellers and buyers are treated symmetrically in that all agents are allowed to behave strategically—no price-taking assumptions are imposed a priori —and, departing from the Walrasian tradition, the price is constructed from agents strategic decisions.

4 Simultaneous bilateral oligopoly

As stressed in the introduction, the bilateral oligopoly model is a strategic market game based on a two-commodity exchange economy with corner initial endowments. Footnote 13 We define the exchange economy \(\mathcal {E}=\{(u_i(\cdot ),(x_i^0,y_i^0))_{i=1}^{m+n}\}\) as in the previous section. The strategy set of a seller i is defined as in ( 1 ). The strategy set of a buyer i is

The strategy \(b_i\) is the bid of money that buyer i makes on the consumption good. Let \(\mathcal {B}=\prod _{i=1}^{m+n}\mathcal {B}_i\) and \(\mathcal {B}_{-h}=\prod _{i\ne h}\mathcal {B}_i\) . Let \(\mathbf{b}=(b_{m+1},\dots ,b_{m+n})\) and \(\mathbf{b}_{-i}=(b_{m+1},\dots ,b_{i-1},b_{i+1},\dots ,b_{m+n})\) be elements of \(\mathcal {B}\) and \(\mathcal {B}_{-i}\) respectively. For each \((\mathbf{q},\mathbf{b})\in \mathcal {Q}\times \mathcal {B}\) , the price vector \(\mathbf{p}(\mathbf{q},\mathbf{b})=(p_x(\mathbf{q},\mathbf{b}),1)\) is determined such that the price of the consumption good is given by the ratio of the total money bids made for the good to the total amount of good made available by the sellers:

with \(B=\sum _{i=m+1}^{m+n} b_i\) . Having defined the price formation rule, which is non-Walrasian, we can now define the rules to calculate the commodity bundles of each agent. For each \((\mathbf{q},\mathbf{b})\in \mathcal {Q}\times \mathcal {B}\) , the commodity bundle \((x_i(\mathbf{q},\mathbf{b}),y_i(\mathbf{q},\mathbf{b}))\) of a seller i is given by

for \(i=1,\dots ,m\) , and the commodity bundle \((x_i(\mathbf{q},\mathbf{b}),y_i(\mathbf{q},\mathbf{b}))\) of a buyer i is given by

for \(i=m+1,\dots ,m+n\) . As such, each agent’s amount of the commodity they are endowed with reduces by the quantity of that commodity they offer to the market, and the amount of the other commodity is given by their proportional share of the aggregate amount of that commodity offered by the other side of the market, so sellers receive a share \(q_i/Q\) of the aggregate bid B , and buyers receive a share \(b_i/B\) of the aggregate offer Q . The payoff function of agent i is \(\pi _i(\mathbf{q},\mathbf{b})=u_i(x_i(\mathbf{q},\mathbf{b}),y_i(\mathbf{q},\mathbf{b}))\) , for \(i=1,\dots ,m+n\) . The simultaneous bilateral oligopoly game is then a set \(\Gamma '=\{(\mathcal {Q}_i,\pi _i(\cdot ))_{i=1}^{m},(\mathcal {B}_i,\pi _i(\cdot ))_{i=m+1}^{m+n}\}\) .

The definition of a Cournot-Nash equilibrium in bilateral oligopoly is as follows.

Definition 3

The strategy profile \((\hat{\mathbf{q}},\hat{\mathbf{b}})\) is a Cournot-Nash equilibrium of the game \(\Gamma '\) if for each seller \(i=1,\ldots ,m\) we have \(\pi _i(\hat{q}_i,\hat{\mathbf{q}}_{-i},\hat{\mathbf{b}})\ge \pi _i(q_i,\hat{\mathbf{q}}_{-i},\hat{\mathbf{b}})\) , for each \(q_i\in \mathcal Q_i\) , and for each buyer \(i=m+1,\ldots ,m+n\) we have \(\pi _i(\hat{\mathbf{q}},\hat{b}_i,\hat{\mathbf{b}}_{-i})\ge \pi _i(\hat{\mathbf{q}},b_i,\hat{\mathbf{b}}_{-i})\) , for each \(b_i\in \mathcal B_i\) .

We now consider an example to illustrate the Cournot-Nash equilibrium concept.

Consider the exchange economy defined in Example 2. To find the Cournot-Nash equilibrium, we have to solve the payoff maximisation problems for all agents. We first consider sellers and then buyers. Consider the maximisation problem of seller 1:

This payoff function is strictly concave in \(q_1\) ; we solve as an unconstrained problem then check the solution satisfies the constraints. The first-order condition is

Since all sellers are identical and all buyers are identical, we consider a symmetric Cournot-Nash equilibrium where \(\hat{q}_1=\hat{q}_2=\hat{q}\) and \(\hat{b}_3=\hat{b}_4=\hat{b}\) . Then the previous equation becomes,

and we obtain

Consider next the maximisation problem of buyer 3:

The first order condition of the buyer’s unconstrained maximisation problem can be written as

Since we consider the symmetric Cournot-Nash equilibrium, we then obtain

Study of the second-order conditions reveals the solution corresponds to a maximum. By combining equations ( 7 ) and ( 8 ), we find that the Cournot-Nash equilibrium for the bilateral oligopoly model is

At the Cournot-Nash equilibrium the price vector is \(\mathbf{p}(\hat{\mathbf{q}},\hat{\mathbf{b}})=(\frac{\sqrt{17}-1}{4},1)\) and the allocation is

This example clarifies that the simultaneous bilateral oligopoly model allows us to study oligopoly where all agents are treated symmetrically and no assumptions on their behaviours are made a priori . Indeed, given the structure of the game, all agents act strategically because they can manipulate the price by changing their actions. Therefore, bilateral oligopoly addresses the critique raised by Okuno et al. ( 1980 ). The fact that buyers act strategically is one of the reasons why sellers’ and buyers’ commodity bundles at the Cournot-Nash equilibrium are different from those obtained at the Cournot-Walras equilibrium, even if the exchange economies in Examples 2 and 3 are the same. We stress again that buyers are assumed to behave as price-takers in the Cournot-Walras approach while they are permitted to act strategically in bilateral oligopoly. Furthermore, while the Cournot-Walras model suffers from issues because of the potential discontinuity of the Walras price correspondence, this is not the case in bilateral oligopoly because the price formation rule is non-Walrasian. The existence of a Cournot-Nash equilibrium was studied by Bloch and Ferrer ( 2001a ) and Dickson and Hartley ( 2008 ), who also studied uniqueness of equilibrium. Additionally, Bloch and Ferrer ( 2001b ) showed the existence when all agents have a constant elasticity of substitution utility function.

At this point of the analysis a natural question arises: is it possible to employ the bilateral oligopoly model to study asymmetric oligopoly where no a priori assumptions on agents behaviours are made? In other words, is it possible to develop a framework where the differences in agents’ behaviours arise endogenously in equilibrium? This is also known as the problem of providing a strategic foundation for oligopoly.

In the literature, two main approaches are used to this end. The first approach consists of using mixed exchange economies where large agents (oligopolists) are represented by atoms and small agents (competitive agents) by an atomless continuum. An atom is an agent whose initial endowment is non-negligible compared to the total endowment of the economy while an agent in the continuum holds only a negligible part of it. The model was proposed by Gabszewicz and Mertens ( 1971 ) and Shitovitz ( 1973 ) in cooperative game theory. Shitovitz ( 1973 ) stated:

“The main point in our treatment is that the small and the large traders are not segregated into different groups a priori; they are treated on exactly the same basis. The distinctions we have found between them are an outcome of the analysis; they have not been artificially introduced in the beginning, as is the case in the classical approach.”

This approach based on mixed exchange economies was also extended to noncooperative game theory by Okuno et al. ( 1980 ), in order to address their critique, and further generalised by Busetto et al. ( 2011 ) and Busetto et al. ( 2018 ). Busetto et al. ( 2020 ) undertake a study of bilateral oligopoly in a mixed exchange economy. In this setting, while all agents have a priori the same strategic position, they found that in equilibrium large agents represented by atoms have market power while small agents on the continuum behave as if they are price-takers.

The second approach is based on considering partial replicas of exchange economies where the number of some agents is increased while proportionally reducing their weights. This method was introduced to bilateral oligopoly by Dickson and Hartley ( 2013a ) and it was subsequently formalized, using the tools of measure theory, by Busetto et al. ( 2017 ). The main result of this approach is that agents who are replicated gradually lose their ability to influence prices as their number increases and in the limit they behave as price takers, whereas agents that are not replicated and remain large retain their market power.

In the last part of this section, we consider the second approach and study the limit of partial replicas where we replicate only the set of buyers. We study such a limit because it represents an asymmetric oligopoly where buyers are asymptotically negligible and so should behave as price takers. Consider an exchange economy \(\mathcal {E}=\{(u_i(\cdot ),(x_i^0,y_i^0))_{i=1}^{m+n}\}\) where the first m agents are sellers and all other n agents are buyers. The partially replicated exchange economy \(\mathcal {E}^r\) consists in an exchange economy having the same sellers as \(\mathcal {E}\) and r replicas of each buyer in \(\mathcal {E}\) . Furthermore, to each buyer is associated a weight \(\frac{1}{r}\) which is used to weight buyers when aggregating across them. It is then clear that the aggregate bid must include the weighting factor \(\frac{1}{r}\) when partially replicating the economy. For clarity, we denote by \(\tilde{B}=\sum _{i=m+1}^{m+n}\sum _{j=1}^r\frac{1}{r}b_{ij}\) the weighed sum of bids where \(b_{ij}\) is the bid of the j th replica of buyer i . This kind of partial replica based on reducing the weight of each buyer as the number of replicas increases allows us to increase the number of buyers, consequently reducing their market power, without the undesirable consequence of the demand for the consumption good exploding while its supply remains fixed (as the number of sellers is fixed) and the price consequently tending to infinity. Footnote 14

Note that given the price formation rule ( 6 ) and the definition of \(\tilde{B}\) , if r increases, then the buyers’ ability to influence prices decreases and at the limit, for \(r\rightarrow \infty\) , totally disappears. Obviously we have that \(\mathcal {E}=\mathcal {E}^1\) . It is important to stress that the limit of a sequence of Cournot-Nash equilibria, which is denoted by \((\bar{\mathbf {q}},\bar{\mathbf {b}})\) , is not a Cournot-Nash equilibrium of the limit economy as the underlying game in the limit is not well-defined. Nevertheless, the limit of the sequence gives us an object that can be compared to the other solution concepts in finite economies.

We now consider an example to illustrate how to partially replicate an exchange economy and how to calculate its limit.

Consider the partial replica of the exchange economy defined in Example 2 with r replicas of each buyer. We then have an exchange economy with 2 sellers and 2 r buyers, i.e., \(u_i(x,y)=\ln (1+x)+y\) and \((x_i^0,y_i^0)=(3,0)\) , for \(i=1,2\) and \(u_{ij}(x,y)=3x-\frac{1}{2}x^2+y\) and \((x_{ij}^0,y_{ij}^0)=(0,5)\) , for \(i=3,4\) and \(j=1,\dots ,r\) . As each buyer has a weight \(\frac{1}{r}\) , we have that \(\tilde{B}=\sum _{j=1}^{r}\frac{1}{r}b_{3j}+\sum _{j=1}^{r}\frac{1}{r}b_{4j}\) . To simplify the analysis, we consider a symmetric Cournot-Nash equilibrium, where all buyers play the same strategy, and then \(\hat{\tilde{B}}=2\hat{b}\) . But then, if we consider the sellers’ payoff maximisation problems, it is straightforward to verify that in a symmetric equilibrium sellers’ strategies are as in the previous example

On the contrary, buyers’ maximisation problems are different from the previous example because now there are 2 r buyers instead of two. Consider the maximisation problem of buyer 3 h , i.e., the replica h of buyer 3:

Since we consider a symmetric Cournot-Nash equilibrium where \(\hat{q}_1=\hat{q}_2=\hat{q}\) and \(\hat{b}_{3j}=\hat{b}_{4j}=\hat{b}\) for \(j=1,\dots ,r\) , from the previous equation we obtain

Let \(k=1-\frac{1}{2r}\) . By combining equations ( 9 ) and ( 12 ), we obtain the following Cournot-Nash equilibrium for the bilateral oligopoly model

The limit of this Cournot-Nash equilibrium as \(r\rightarrow \infty\) is \(\bar{q}_{i}=2\) for sellers and \(\bar{b}_{ij}=2\) for buyers. At the limit the price vector is \(\mathbf{p}(\bar{\mathbf{q}},\bar{\mathbf{b}})=(1,1)\) and the sellers’ and buyers’ commodity bundles are

We finally remark that the allocation

for the partially replicated exchange economy \(\mathcal {E}^r\) is feasible for any r as the market clearing conditions are satisfied, i.e.,

It is immediate to see that the commodity bundles at the limit of the Cournot-Nash equilibrium are different from the ones at the Cournot-Walras equilibrium of Example 2. This result is somewhat surprising as at the limit of the Cournot-Nash equilibrium buyers have no influence on the price, as is assumed in the Cournot-Walras approach, yet the equilibrium allocations differ. This is due to the fact that the Cournot-Walras approach has an intrinsic two-stage structure—sellers decide their supply taking into account their influence on the Walrasian demands of buyers—whereas when considering a Cournot-Nash equilibrium in the bilateral oligopoly model all agents choose their actions simultaneously so sellers must form beliefs about how the buyers will behave. This fact was stressed by Dickson and Hartley ( 2013a ) who considered the conditions under which the two models coincide in the limit, and when they do not. In mixed exchange economies, Codognato ( 1995 ) and Busetto et al. ( 2008 ) showed that the allocation at a Cournot-Walras equilibrium is different from the one at a Cournot-Nash equilibrium of the Shapley window model. Therefore, we can conclude that the bilateral oligopoly model can be useful to study simultaneous asymmetric oligopoly in a closed market model by partially replicating the underlying exchange economy but it does not provide a foundation of the Cournot-Walras approach. In the next section, we address this last issue by studying a sequential bilateral oligopoly model.

5 Sequential bilateral oligopoly

In this section we consider a sequential-move bilateral oligopoly model with a two-stage structure where the timing of the model is exogenously specified as follows: in the first stage sellers simultaneously choose the quantities of the consumption good to put up in exchange for money; in the second stage, after observing all sellers’ offers, the buyers simultaneously choose the quantity of money to bid for the consumption good. At the end of the second stage bids and offers are aggregated and the price is determined according to the usual rule in ( 6 ). Groh ( 1999 ) first considered a sequential reformulation of bilateral oligopoly in the context of an example, that was extended to general settings in Dickson ( 2006 ). Footnote 15

We first consider an exchange economy \(\mathcal {E}=\{(u_i(\cdot ),(x_i^0,y_i^0))_{i=1}^{m+n}\}\) and we then define the sequential bilateral oligopoly. The strategy set of a seller i is defined as in ( 1 ). The strategy set of a buyer i is

Let \(\mathcal {B}=\prod _{i=m+1}^{m+n}\mathcal {B}_i\) and \(\mathbf{b}(\cdot )=(b_{m+1}(\cdot ),\dots ,b_{m+n}(\cdot ))\) be an element of \(\mathcal {B}\) . For each \((\mathbf{q},\mathbf{b}(\mathbf{q}))\in \mathcal {Q}\times \mathcal {B}\) , the price vector \(\mathbf{p}(\mathbf{q},\mathbf{b}(\mathbf{q}))=(p_x(\mathbf{q},\mathbf{b}(\mathbf{q})),1)\) is such that

with \(B(\mathbf{q})=\sum _{i=m+1}^{m+n} b_i(\mathbf{q})\) . For each \((\mathbf{q},\mathbf{b}(\mathbf{q}))\in \mathcal {Q}\times \mathcal {B}\) , the commodity bundle \((x_i(\mathbf{q},\mathbf{b}(\mathbf{q})),y_i(\mathbf{q},\mathbf{b}(\mathbf{q})))\) of a seller i is given by

for \(i=1,\dots ,m\) , and the commodity bundle \((x_i(\mathbf{q},\mathbf{b}(\mathbf{q})),y_i(\mathbf{q},\mathbf{b}(\mathbf{q})))\) of a buyer i is given by

for \(i=m+1,\dots ,m+n\) . The payoff function of an agent i is \(\pi _i(\mathbf{q},\mathbf{b}(\mathbf{q}))=u_i(x_i(\mathbf{q},\mathbf{b}(\mathbf{q})),\) \(y_i(\mathbf{q},\mathbf{b}(\mathbf{q})))\) , for \(i=1,\dots ,m+n\) . The sequential bilateral oligopoly model is then a set \(\Gamma ''=\{(\mathcal {Q}_i,\pi _i(\cdot ))_{i=1}^{m},(\mathcal {B}_i,\pi _i(\cdot ))_{i=m+1}^{m+n}\}\) .

We now define a subgame-perfect Nash equilibrium (hereafter SPNE) which is the equilibrium concept we use in this dynamic game.

Definition 4

A strategy profile \((\hat{\mathbf{q}},\hat{\mathbf{b}}(\hat{\mathbf{q}}))\) is a SPNE for \(\Gamma ''\) if and only if it is a Cournot-Nash equilibrium in every subgame of the game \(\Gamma ''\) .

Note that in the sequential bilateral oligopoly the subgames are the whole game and the subgames in which buyers choose their optimal bids following any vector of offers from the sellers. We now consider an example to illustrate how to find the SPNE and how to find the limit of a sequence of SPNE when we partially replicate the exchange economy. We stress again that the limit is not a SPNE as the underlying game is not well-defined at the limit.

Consider the same partially replicated exchange economy defined in Example 4. As before, to simplify the analysis, we consider a symmetric SPNE that can be computed as follows. We first find a symmetric Nash equilibrium among the buyers for any feasible strategies of the sellers (i.e., in any buyers’ subgame). We then substitute the equilibrium strategies of the buyers in the sellers’ payoff functions to determine their reaction functions given the responses of the buyers, after which we can find mutually consistent best responses among the sellers. The strategy profile obtained by this method is a SPNE. It is immediate to verify that each buyer’s maximisation problem is as in ( 10 ). Therefore the best response of the buyer 3 h solves the first order condition in ( 11 ) which becomes in this case

Since we consider a symmetric SPNE where \(\hat{b}_{3j}(\mathbf{q} )=\hat{b}_{4j}(\mathbf{q} )=\hat{b}(\mathbf{q} )\) for \(j=1,\dots ,r\) , from the previous equation we obtain

with \(k=1-\frac{1}{2r}\) . Consider next the maximisation problem of seller 1. If we substitute the strategy \(\hat{b}(\mathbf{q} )\) in the seller’s payoff function we obtain

The first order condition of the seller’s unconstrained maximisation problem is

Since we consider a symmetric SPNE where \(\hat{q}_1=\hat{q}_2=\hat{q}\) , the previous equation implies

Therefore, by combining equations ( 14 ) and ( 15 ), we obtain the following SPNE for the sequential bilateral oligopoly

The limit of the SPNE for \(r\rightarrow \infty\) is \(\bar{q}_{i}=\frac{9-\sqrt{15}}{3}\) for sellers and \(\bar{b}_{ij}(\bar{\mathbf{q }})=\frac{3\sqrt{15}-5}{3}\) for buyers. At the limit the price vector is \(\mathbf{p}(\bar{\mathbf{q}},\bar{\mathbf{b}}(\bar{\mathbf{q}}))=(\frac{\sqrt{15}}{3},1)\) and the sellers’ and buyers’ commodity bundles are

It is immediate to see that the commodity bundles at the limit of the SPNE are different to those at the limit of the Cournot-Nash equilibrium in which moves are simultaneous, but are the same as those at the Cournot-Walras equilibrium. We stress again that in this framework all agents are treated symmetrically and the different behaviours of sellers and buyers are obtained endogenously at the limit of the SPNE. With this last example, we have shown that sequential bilateral oligopoly in which it is exogenously specified that sellers move first and buyers move second can provide a closed market model to study asymmetric oligopoly in which the buyers are assumed to behave as price takers by partially replicating the underlying exchange economy. Furthermore, this model can provide a foundation for the Cournot-Walras approach. It is worth stressing that the price equation ( 13 ) in the many buyer limit corresponds to the inverse demand function in Example 1. In mixed exchange economies, Busetto et al. ( 2008 ) showed that the set of the Cournot-Walras equilibrium allocations coincides with a particular subset of SPNE allocations of the two-stage reformulation of the Shapley window model.

6 Walras equilibrium and welfare

The Walrasian analysis in the synthesis reached in the contributions of Debreu ( 1959 ), Arrow and Hahn ( 1971 ) and McKenzie ( 2002 ) crucially relies on the assumption of price-taking, i.e., all agents are assumed to behave competitively. It is then important to study under which conditions on the fundamentals of an economy agents consider prices as given endogenously in equilibrium, without making ad hoc assumptions. This is the problem of providing a strategic foundation for perfect competition, which is similar in spirit to the problem of finding a foundation for models of oligopoly. In fact, a strategic foundation for perfect competition can also be provided by considering continuum exchange economies or replicated exchange economies. Footnote 16 In cooperative game theory Aumann ( 1964 ) provided a foundation for perfect competition in economies with a continuum of agents by showing an equivalence result between the core and the Walras allocation. Subsequently, in noncooperative game theory, Dubey and Shapley ( 1994 ) and Codognato and Ghosal ( 2000 ) considered strategic market games with a continuum of agents and they show equivalence results between the Cournot-Nash and Walras allocations. Those results are based on the fact that when there is a continuum of agents everyone is negligible and cannot influence prices. The second approach based on replicated exchange economies was pioneered in cooperative game theory by Edgeworth ( 1881 ) and further analysed by Debreu and Scarf ( 1963 ). Footnote 17 Subsequently, Dubey and Shubik ( 1978 ), Sahi and Yao ( 1989 ), and Amir et al. ( 1990 ) applied this technique to strategic market games. They show that when all agents in the economy are replicated the allocation at the limit of the Cournot-Nash equilibrium corresponds to the allocation at the Walras equilibrium. Those results are heuristically based on the fact that when the number of agents increases their influence on prices decreases and in the limit totally disappears. Footnote 18

We now show how the bilateral oligopoly model can be employed to provide a foundation for perfect competition by considering replicated exchange economies. Consider the exchange economy \(\mathcal {E}=\{(u_i(\cdot ),(x_i^0,y_i^0))_{i=1}^{m+n}\}\) . A replicated exchange economy consists in an exchange economy where all agents of \(\mathcal {E}\) are replicated r times. We now define the Walras equilibrium concept.

Definition 5

A Walras equilibrium is a pair \((p^*,(x_i^*,y_i^*)_{i=1}^{n+m})\) of a price vector and an allocation such that each commodity bundle \((x_i^*,y_i^*)\) maximises agent i ’s utility function within their budget set, for \(i=1,\dots ,m+n\) , and all markets clear, i.e., \(\sum _{i=1}^{m+n} x_i^*=\sum _{i=1}^{m+n}x_i^0\) and \(\sum _{i=1}^{m+n} y_i^*=\sum _{i=1}^{m+n}y_i^0\) .

From the results in the previous literature, we can conjecture that in replicated exchange economies all agents lose market power and at the limit for \(r\rightarrow \infty\) they all behave competitively. We now consider an example to illustrate this point by showing that the sellers’ and buyers’ commodity bundles at the limit of the Cournot-Nash equilibrium correspond to the ones at the Walras equilibrium.

Consider the replica of the exchange economy defined in Example 2. We then have an exchange economy with 2 r sellers and 2 r buyers, i.e., \(u_{ij}(x,y)=\ln (1+x)+y\) and \((x_{ij}^0,y_{ij}^0)=(3,0)\) , for \(i=1,2\) and \(j=1,\dots ,r\) and \(u_{ij}(x,y)=3x-\frac{1}{2}x^2+y\) and \((x_{ij}^0,y_{ij}^0)=(0,5)\) , for \(i=3,4\) and \(j=1,\dots ,r\) . The Walras equilibrium of the replicated exchange economy is Footnote 19

By following the same steps as in Example 3, we obtain a Cournot-Nash equilibrium

such that \(\hat{q}_{ij}=\frac{7k-\sqrt{k^2+4}}{2k}\) for \(i=1,2\) and \(j=1,\dots ,r\) and \(\hat{b}_{ij}=\frac{2k\sqrt{k^2+4}-2k^2-1}{k}\) for \(i=3,4\) and \(j=1,\dots ,r\) with \(k=1-\frac{1}{2r}\) . The limit of this Cournot-Nash equilibrium as \(r\rightarrow \infty\) is \(\bar{q}_{ij}=\frac{7-\sqrt{5}}{2}\) for sellers and \(\bar{b}_{ij}=2\sqrt{5}-3\) for buyers. At the limit the price vector is \(\mathbf{p} (\bar{\mathbf{q }},\bar{\mathbf{b }})=(\frac{\sqrt{5}-1}{2},1)\) and the sellers’ and buyers’ commodity bundles are

It is immediate to see that the commodity bundles at the limit of the Cournot-Nash equilibrium correspond to the ones at the Walras equilibrium of the underlying exchange economy. This example further clarifies that the assumption of competitive behaviour is justified when there are many of each type of agent.

It is worth noting that this convergence to the Walras equilibrium in terms of commodity bundles, when all agents are replicated, is also obtained with the Cournot-Walras equilibrium and the SPNE. These results, obtained for particular examples, suggest that the timing of the model is not relevant when considering a foundation for perfect competition. Lahmandi-Ayed ( 2001 ) proved the converge of a Cournot-Walras equilibrium to the Walras equilibrium in exchange economies. As mentioned above, Dubey and Shubik ( 1978 ), Amir et al. ( 1990 ), and Sahi and Yao ( 1989 ) studied the converge of a Cournot-Nash equilibrium to the Walras equilibrium in strategic market games. Koutsougeras and Meo ( 2018 ) considered the convergence of a Cournot-Nash equilibrium to the Walras equilibrium for general sequences of economies whose distribution of characteristics has compact support by using the model developed by Postlewaite and Schmeidler ( 1978 ) and Peck et al. ( 1992 ).

We conclude this section by making some welfare considerations on the equilibrium concepts used throughout the paper. First of all, by the first welfare theorem, the Walras equilibrium is Pareto efficient. In contrast, all other allocations found in Examples 2–5 are Pareto inefficient: it is possible to find other commodity bundles which Pareto dominate them. In the following table we report the utility levels of sellers and buyers in the different examples.

It is interesting to note that at the Walras equilibrium, the only efficient equilibrium, sellers get the lowest utility while buyers get the highest. Furthermore, sellers get the highest utility at the Cournot-Walras equilibrium (which is the same as the limit of the SPNE in sequential bilateral oligopoly) which means that, in our examples, they are better off when they face competitive buyers in a sequential oligopoly. We finally remark that Examples 2–6 belong to the general equilibrium framework while Example 1 is a model of partial analysis. For this reason the efficiency of that model cannot be evaluated by using the notion of Pareto efficiency.

7 Conclusion

In this paper we have provided a unified framework to compare different equilibrium concepts to study imperfect competition in exchange economies. We have also clarified the differences among symmetric, asymmetric, simultaneous, and sequential oligopoly and analysed the relationships among them in terms of replicated exchange economies and equilibrium concepts.

By studying our examples we have found some interesting facts. We have seen that bilateral oligopoly can be used to provide a strategic foundation for asymmetric oligopoly models that impose price taking assumptions on some agents, but that this requires a particular timing structure in that those agents that are assumed to be price takers, and are replicated, must move last. Bilateral oligopoly can also be used to provide a strategic foundation for models that assume price taking for all agents, where in contrast timing does not matter. The study of a general strategic foundation for asymmetric oligopoly models will continue to be an interesting area for future research.

It is important to remark that asymmetric oligopoly can be studied by using the partial replica or by considering mixed exchange economies. This alternative approach was introduced by Okuno et al. ( 1980 ) and further scrutinised by Busetto et al. ( 2008 , 2011 , 2017 ) and Busetto et al. ( 2018 , 2020 ).

Our main focus has been on exchange economies because economies with production raise many theoretical and technical problems (see Hart ( 1985 ), Gary-Bobo ( 1988 ), Bonanno ( 1990 ) for a survey). To the best of our knowledge, the only contributions on strategic market games with production are Dubey and Shubik ( 1977 ) and Chen et al. ( 2017 ). A simpler approach was proposed by Gabszewicz and Michel ( 1997 ) (see also Dickson and Hartley ( 2013a )) which considers bilateral oligopoly where only some agents (the sellers) are endowed with a production technology. We leave for further research the study of the different kinds of imperfect competition considered here in economies with production. It is worth highlighting that in a framework with production it is possible to study the differences between sellers maximizing profits and seller maximizing utility functions. This is a classical issue in general equilibrium with imperfect competition. Furthermore, we have restricted our analysis to exchange economies with only two commodities because in a framework with more commodities the results depend on the particular type of strategic market game adopted.

We have discussed related contributions studying the core of exchange economies. This approach, belonging to cooperative game theory, differs from strategic market games which are non-cooperative games. Koutsougeras and Ziros ( 2008 ) and Ziros ( 2011 ) worked on blending the cooperative approach with strategic market games in atomless continuum economies by considering the core and the Mas-Colell bargaining set respectively. We think that this line of research is very important to shed some light on these two different approaches that can be used to study imperfect competition in bilateral oligopolies but also in more general exchange economies. Indeed, Ziros ( 2011 ) remarked that further interesting insights may be obtained with his approach by considering economies with a finite number of agents.

We conclude by mentioning that there is a small literature on experiments in bilateral oligopoly whose contributions are Duffy et al. ( 2011 ) and Barreda-Tarrazona et al. ( 2018 ). We expect this line of inquiry to become more popular in the coming years.

Change history

17 september 2022.

A Correction to this paper has been published: https://doi.org/10.1007/s00712-022-00805-8

Dickson ( 2013b ) shows that examples with Cobb-Douglas utility functions, very common in the literature, have very peculiar features which do not hold in general.

A strategic market game with trading post and fiat money was considered by Postlewaite and Schmeidler ( 1978 ) and Peck et al. ( 1992 ).

See Gale ( 2000 ) for a discussion on why the study of the foundations of perfect competition is important.

In contrast to the classical partial equilibrium analysis, we consider sellers as being endowed with the good and deciding how much of that good to send to market in exchange for commodity money to maximize their utility of consumption, rather than maximizing profit after defining a cost function. We do so because in the rest of the paper we deal with two commodity exchange economies, a simple general equilibrium framework in which the availability of the two goods is fixed and sellers are characterized by their holdings of the good (rather than their production technologies) and we consider agents whose utility depends positively on both commodities.

Commodity y should be called commodity money because it enters in the utility function. However, for simplicity, we simply refer to it as money.

Pantaleoni ( 1908 ) pointed out that Leon Walras was dissatisfied by the “approximative way” in which the demand curve was introduced by Cournot in his analysis.

More generally, Walrasian demands can be correspondences which associate to each price the set of commodity bundles which maximise the utility function in the budget set. For the sake of simplicity, we just consider the case in which Walrasian demands are functions.

Note that this maximisation problem has a solution only for continuous utility functions and positive prices.

To avoid cumbersome notation, but without confusion, we denote the same elements of different models with the same symbol.

We use quadratic utility functions as the implied demand function from the buyers is then linear. Note that each buyer’s utility function reaches a point of saturation at \(x=3\) ; however, as the total endowment of commodity x is 6 and we consider two symmetric buyers we will not be in danger of examining solutions that breach this saturation point.

It is worth noting that, since the utility functions are quasi-linear, there can be corner solutions. However, for the sake of simplicity and since this does not affect our analysis, we just consider interior solutions.

A further shortcoming of the Cournot-Walras approach is that it is extremely challenging to obtain a general existence result because oligopolists influence prices by manipulating the Walras price correspondence which may fail to be continuous unless strict assumptions are imposed on the set of price-taking agents. Nevertheless, some existence results have been obtained in particular frameworks: Bonisseau and Florig ( 2003 ) proved the existence of a Cournot-Walras equilibrium in linear exchange economies; Codognato and Julien ( 2013 ) proved the existence in mixed exchange economies where agents on the continuum have Cobb-Douglas utility functions; and Shirai ( 2010 ) proves the existence of a Cournot-Walras equilibrium in production economies.

Bloch and Ferrer ( 2001a ) and Dickson and Hartley ( 2013b ) also consider the case in which agents are endowed with both commodities, i.e. have “interior” initial endowments, and can choose whether they become sellers or buyers.

The weighting is used whenever aggregating across the set of buyers—to construct the aggregate bid as we explained, and also in the aggregation of buyers’ endowments and demands when considering market clearing, which therefore takes place at a per-replica level. In the replicated exchange economy \(\mathcal {E}^r\) an allocation is feasible if it satisfies the following market clearing conditions

These equations further clarify the role of the weight in avoiding that the demand for the consumption good and the endowment of commodity 2 explode. Furthermore, they also show that there is clear analogy between the weight \(\frac{1}{r}\) and the measure of an atom in mixed exchange economies. The interested reader should refer to Busetto et al. ( 2017 ) and their definition of partial replica à la Cournot.

Dickson and Hartley ( 2013a ) consider a sequential market share game and Busetto et al. ( 2008 ) consider a sequential reformulation of the Shapley window model.

These different approaches are illustrated by the distinction between limit theorems and theorems in the limit (see Gale ( 2000 )). See Mas-Colell ( 1982 ) for a study on the links between the two approaches.

Note that this replica differs from the partial replica defined in Sect.  4 in two respects: all agents in the economy are replicated and it does not require to associate a weight to each agent.

Mas-Colell ( 1980 ) surveyed the main contributions on the foundations of perfect competition by considering other noncooperative approaches that do not rely on strategic market games.

It is straightforward to verify that sellers’ and buyers’ commodity bundles are the same for any r .

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Dickson, A., Tonin, S. An introduction to perfect and imperfect competition via bilateral oligopoly. J Econ 133 , 103–128 (2021). https://doi.org/10.1007/s00712-020-00727-3

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