Oligopoly and Game Theory
Dr. Amy McCormick Diduch
Oligopoly and market structure
An oligopoly consists of a small number of firms producing for the same market. Defining characteristics include barriers to entry (which protect any resulting profits) and patterns of strategic interaction among the firms.
To identify “strategic interactions,” it helps to understand why perfectly competitive firms are not interacting strategically. In a perfectly competitive market, firms do one thing: equate the market-generated price (determined through interactions of many buyers and sellers) to their own marginal cost of production to find their profit-maximizing level of output. That’s it. No marketing, no price wars, no strategizing about how to out-sell the competition. Why? Perfectly competitive markets are made up of many, many small firms producing identical products. They have no ability to choose a different price and they receive no benefit from marketing a product that is indistinguishable from all the others.
Monopolistically competitive markets are made up of a large number of firms producing differentiated products. (The market for t-shirts might fall into this category, because t-shirts from different companies are substitutes for each other but not identical – the definition of “differentiated”). These firms engage in activities aimed increasing demand for their own product. Because these products are differentiated, buyers can form preferences for one company’s version over another’s. Advertising, the creation and expansion of brand identities, and the formation of “entry level” to “elite level” classes of goods are all associated with monopolistically competitive firms. However, barriers to entry remain low in this market structure, pushing profits towards zero. The large number of firms in the market makes strategic targeting difficult. No single brand is large enough – or identifiable enough – to become the primary target of competition. (Hint: if you can name all of the major brands in a market, it probably isn’t monopolistically competitive. It is most likely an oligopoly).
Oligopoly is different, then, because the small number of firms (protected by barriers to entry) means that any individual firm will think carefully about how the actions it takes will influence actions taken by its competitors. An oligopolistic firm has the power to lower its price, but it must take into account how competitors will react. It might want to expand its operations, but will do so only after thinking about whether competitors might do the same. The presence of strategic thinking makes this market structure more challenging to analyze. There isn’t a simple rule of thumb (such as “set marginal revenue equal to marginal cost”) that will predict prices, output levels or profits for oligopolies.
Microeconomic theorists have created a variety of models to depict specific types of interactions that may be present in oligopolies. For example, the model of Bertrand competition demonstrates that a price war between duopolists (an oligopoly with only two firms) can result in an outcome identical to that of perfect competition, with price equal to marginal cost and profits driven to zero. The “kinked demand curve” model of oligopoly can explain why prices of some goods tend to be “sticky:” any decrease in price is met by competitors but any increase in price is not, so changing price in either direction lowers profits.
Game theory
One of the most interesting tools for thinking about strategic interactions is known as game theory. First developed by mathematician John von Neumann, it provides a way to think logically about the choices players should make to bring about the best possible outcomes. Game theory emphasizes the interdependence of the players: the outcome of any game depends on your own choices AND the choices made by your competitors. Knowing this, you will take your competitors’ actions into account when choosing your own strategies.
If you’ve played any game, you already know some of the basic ideas. First, there are rules of play. In tic-tac-toe, the rules say that you make one mark in an empty space on your turn. In business, the rules are laws and regulations as well as social norms. Second, there are differences in the amount information available to you as you play. In tic-tac-toe, you directly observe the actions of your opponent. In the card game Uno, you do not know what cards are held by your opponent. In market competition, some actions taken by your competitors are observable while others are hidden and must be surmised. Third, competitors have certain goals. In tic-tac-toe, the goal is to get three of your marks in a row and be declared the winner. In market competition, the goal is generally profit-maximization (at least in the long run; short run losses might strategically lead to long run gains). Finally, the competing firms have various strategies available to them (which could involve price, product innovation, location, etc.).
Game theory problems can be set up in different forms: mathematical equations, decision trees or matrices (tables). Equations are needed for more complex problems but the basic ideas can be conveyed using trees or tables.
Analysis of a game matrix: “best responses”
Here’s a relatively simple game theory problem: two firms compete in the market for lawn mowers. Spring is the big season for lawn mower purchases and the two companies are deciding how to price their lawn mowers next spring. Neither is able to ascertain in advance what price the other company will choose. Thus, these companies are choosing their prices simultaneously (an important point to specify in a game theory problem. The alternative is that the companies choose sequentially, meaning that one company can observe the choice of another). Each firm wants to maximize its own profits for the upcoming sales season.
I’m naming these companies Mow Better and Smooth Green. Their strategies are “High price” and “Low price” for the spring lawn mower season and the payoffs are their expected profits. The game matrix below presents these profits. There are two companies that choose between two strategies, resulting in four possible outcomes for this game. Mow Better’s two strategies are listed in the left column while Smooth Green’s two strategies are listed in the top row. Each payoff square in the table provides the expected profits for any two joint strategies. For example, if Mow Better chooses Low spring prices when Smooth Green chooses High spring prices, Mow Better will make $6 million and Smooth Green will make $1 million.
Dr. Amy McCormick Diduch
Oligopoly and market structure
An oligopoly consists of a small number of firms producing for the same market. Defining characteristics include barriers to entry (which protect any resulting profits) and patterns of strategic interaction among the firms.
To identify “strategic interactions,” it helps to understand why perfectly competitive firms are not interacting strategically. In a perfectly competitive market, firms do one thing: equate the market-generated price (determined through interactions of many buyers and sellers) to their own marginal cost of production to find their profit-maximizing level of output. That’s it. No marketing, no price wars, no strategizing about how to out-sell the competition. Why? Perfectly competitive markets are made up of many, many small firms producing identical products. They have no ability to choose a different price and they receive no benefit from marketing a product that is indistinguishable from all the others.
Monopolistically competitive markets are made up of a large number of firms producing differentiated products. (The market for t-shirts might fall into this category, because t-shirts from different companies are substitutes for each other but not identical – the definition of “differentiated”). These firms engage in activities aimed increasing demand for their own product. Because these products are differentiated, buyers can form preferences for one company’s version over another’s. Advertising, the creation and expansion of brand identities, and the formation of “entry level” to “elite level” classes of goods are all associated with monopolistically competitive firms. However, barriers to entry remain low in this market structure, pushing profits towards zero. The large number of firms in the market makes strategic targeting difficult. No single brand is large enough – or identifiable enough – to become the primary target of competition. (Hint: if you can name all of the major brands in a market, it probably isn’t monopolistically competitive. It is most likely an oligopoly).
Oligopoly is different, then, because the small number of firms (protected by barriers to entry) means that any individual firm will think carefully about how the actions it takes will influence actions taken by its competitors. An oligopolistic firm has the power to lower its price, but it must take into account how competitors will react. It might want to expand its operations, but will do so only after thinking about whether competitors might do the same. The presence of strategic thinking makes this market structure more challenging to analyze. There isn’t a simple rule of thumb (such as “set marginal revenue equal to marginal cost”) that will predict prices, output levels or profits for oligopolies.
Microeconomic theorists have created a variety of models to depict specific types of interactions that may be present in oligopolies. For example, the model of Bertrand competition demonstrates that a price war between duopolists (an oligopoly with only two firms) can result in an outcome identical to that of perfect competition, with price equal to marginal cost and profits driven to zero. The “kinked demand curve” model of oligopoly can explain why prices of some goods tend to be “sticky:” any decrease in price is met by competitors but any increase in price is not, so changing price in either direction lowers profits.
Game theory
One of the most interesting tools for thinking about strategic interactions is known as game theory. First developed by mathematician John von Neumann, it provides a way to think logically about the choices players should make to bring about the best possible outcomes. Game theory emphasizes the interdependence of the players: the outcome of any game depends on your own choices AND the choices made by your competitors. Knowing this, you will take your competitors’ actions into account when choosing your own strategies.
If you’ve played any game, you already know some of the basic ideas. First, there are rules of play. In tic-tac-toe, the rules say that you make one mark in an empty space on your turn. In business, the rules are laws and regulations as well as social norms. Second, there are differences in the amount information available to you as you play. In tic-tac-toe, you directly observe the actions of your opponent. In the card game Uno, you do not know what cards are held by your opponent. In market competition, some actions taken by your competitors are observable while others are hidden and must be surmised. Third, competitors have certain goals. In tic-tac-toe, the goal is to get three of your marks in a row and be declared the winner. In market competition, the goal is generally profit-maximization (at least in the long run; short run losses might strategically lead to long run gains). Finally, the competing firms have various strategies available to them (which could involve price, product innovation, location, etc.).
Game theory problems can be set up in different forms: mathematical equations, decision trees or matrices (tables). Equations are needed for more complex problems but the basic ideas can be conveyed using trees or tables.
Analysis of a game matrix: “best responses”
Here’s a relatively simple game theory problem: two firms compete in the market for lawn mowers. Spring is the big season for lawn mower purchases and the two companies are deciding how to price their lawn mowers next spring. Neither is able to ascertain in advance what price the other company will choose. Thus, these companies are choosing their prices simultaneously (an important point to specify in a game theory problem. The alternative is that the companies choose sequentially, meaning that one company can observe the choice of another). Each firm wants to maximize its own profits for the upcoming sales season.
I’m naming these companies Mow Better and Smooth Green. Their strategies are “High price” and “Low price” for the spring lawn mower season and the payoffs are their expected profits. The game matrix below presents these profits. There are two companies that choose between two strategies, resulting in four possible outcomes for this game. Mow Better’s two strategies are listed in the left column while Smooth Green’s two strategies are listed in the top row. Each payoff square in the table provides the expected profits for any two joint strategies. For example, if Mow Better chooses Low spring prices when Smooth Green chooses High spring prices, Mow Better will make $6 million and Smooth Green will make $1 million.
I’ll used a technique known as “best response” to analyze this game theory table. This is a methodical technique that asks how each company would respond to each possible strategy of its opponent. You ask the same question – how should the opponent respond? – for each possible strategy listed in the game matrix.
To start: how should Mow Better respond if it thinks Smooth Green might set High prices in the spring? The answer is found by examining whether Mow Better’s profits in this scenario would be higher if it charged High or Low prices in response to this decision by Smooth Green. The table below highlights the best response for Mow Better: it would want to charge a Low price in this scenario because the potential for $6 million in profits beats the $4 million expected from charging a High price. To make this easier to see, I've hidden the (temporarily irrelevant) right side of the table and I've circled Mow Better's profits for their best response.
To start: how should Mow Better respond if it thinks Smooth Green might set High prices in the spring? The answer is found by examining whether Mow Better’s profits in this scenario would be higher if it charged High or Low prices in response to this decision by Smooth Green. The table below highlights the best response for Mow Better: it would want to charge a Low price in this scenario because the potential for $6 million in profits beats the $4 million expected from charging a High price. To make this easier to see, I've hidden the (temporarily irrelevant) right side of the table and I've circled Mow Better's profits for their best response.
How should Mow Better respond if it thinks that Smooth Green will choose a Low price for spring? The table below shows that in this scenario, Mow Better’s “best response” is to choose Low price as well, because the $2 million in expected profits is better than the $1 million it would receive if it insisted on choosing a high price. (Again, I've hidden the left half of the table and circled the expected profits from the best response).
Mow Better has a dominant strategy: choose a Low price no matter what Smooth Green Chooses. The table below highlights Mow Better’s optimal responses to each of Smooth Green’s strategies. In both cases, Mow Better should choose a Low spring price:
In general, a dominant strategy is a choice that is always optimal, no matter what an opponent chooses. Many games will not have dominant strategies but when you do find one, it becomes much easier to predict the outcome.
Next we examine Smooth Green’s “best responses.” What should Smooth Green do if it believes that Mow Better will choose High prices for the spring? The table below highlights this scenario (by focusing your attention on Smooth Green's possible responses to a choice of "High prices" from Mow Better). Smooth Green’s best response is to undercut Mow Better by charging low prices. Their expected profits from this choice are circled.
Next we examine Smooth Green’s “best responses.” What should Smooth Green do if it believes that Mow Better will choose High prices for the spring? The table below highlights this scenario (by focusing your attention on Smooth Green's possible responses to a choice of "High prices" from Mow Better). Smooth Green’s best response is to undercut Mow Better by charging low prices. Their expected profits from this choice are circled.
How should Smooth Green respond if it expects Mow Better to choose Low spring prices? The table below highlights this choice. Smooth Green is better off if it meets those Low prices rather than maintaining High prices, since $1.5 million in expected profits from Low is better than $1 million from a choice of High. Smooth Green also has a dominant strategy: charge Low prices in the spring no matter what Mow Better does.
The predicted outcome of this game is that both Mow Better and Smooth Green follow their dominant strategies and set Low spring prices, resulting in profits of $2 million for Mow Better and $1.5 million for Smooth Green. The outcome is highlighted in the full table below. The best responses for each firm are still circled. Notice that the predicted outcome for this game occurs in a square that represents a best response for both firms (i.e. it has two circles in it).
The outcome of this game results in a Nash Equilibrium (named for mathematician John Nash, who first described it).
A Nash Equilibrium is any game theory outcome in which a player, acting solely on its own, could not have selected an alternative strategy that would have made it better off.
Test whether the outcome in our simple problem is a Nash equilibrium by asking yourself whether Mow Better, knowing that Smooth Green has chosen Low prices, would wish to have chosen High prices instead. In other words, does Mow Better regret its choice of Low spring prices given the choice made by Smooth Green? After checking the table, you’ll see that Mow Better would have made only $1 million in profits if it had chosen High rather than the $2 million it receives by charging low. Thus, Mow Better made the best choice possible given the choice of Smooth Green.
A Nash Equilibrium is any game theory outcome in which a player, acting solely on its own, could not have selected an alternative strategy that would have made it better off.
Test whether the outcome in our simple problem is a Nash equilibrium by asking yourself whether Mow Better, knowing that Smooth Green has chosen Low prices, would wish to have chosen High prices instead. In other words, does Mow Better regret its choice of Low spring prices given the choice made by Smooth Green? After checking the table, you’ll see that Mow Better would have made only $1 million in profits if it had chosen High rather than the $2 million it receives by charging low. Thus, Mow Better made the best choice possible given the choice of Smooth Green.
Notice that this equilibrium does not result in the highest combined profits for the two firms. They would each be better off if they both charged high prices. Why don’t they? Because this scenario would require cooperation (known in the business world as collusion, which is illegal).
Imagine that our two firms find a way to collude and agree to set high prices. Their expected profits are certainly higher than if they end up at the Nash equilibrium. Both companies are happy, right?
Imagine that our two firms find a way to collude and agree to set high prices. Their expected profits are certainly higher than if they end up at the Nash equilibrium. Both companies are happy, right?
What would you do if you ran Mow Better? Knowing that Smooth Green has committed to High prices, might you be tempted to “cheat” on your collusive agreement and set Low prices anyway? Your profits would increase by 50%. Smooth Green has a similar temptation to cheat on your agreement to charge High prices. In general, we expect that collusive agreements will come under pressure due to temptations to cheat and gain higher short term profits. Cheating on the collusive agreement pushes the outcome back to the Nash Equilibrium.
Quiz yourself:
See if you can find the “best responses” using the following game matrix for two cereal manufacturers. They are deciding whether to run new advertising campaigns for their products. The expected profits for Crunchy Oats and Sweet Wheat are provided for each combination of strategies.
Quiz yourself:
See if you can find the “best responses” using the following game matrix for two cereal manufacturers. They are deciding whether to run new advertising campaigns for their products. The expected profits for Crunchy Oats and Sweet Wheat are provided for each combination of strategies.
Ask yourself the following:
Answers:
To determine whether Crunchy Oat has a dominant strategy, find their “best response” to each of Sweet Wheat’s strategies. If Sweet Wheat chooses to Advertise, what would Crunchy Oat want to do? They will prefer to Advertise as well (for expected profit of $8 million, which beats the expected profit of $6 million if they don’t Advertise). If Sweet Wheat chooses Don’t Advertise, what would Crunchy Oat want to do? They will still choose to Advertise, since the $9 million expected profit is better than the $7 million from choosing Don’t Advertise. Thus, Crunchy Oat has a dominant strategy: Advertise.
Does Sweet Wheat have a dominant strategy? If Crunchy Oat chooses to Advertise, what would Sweet Wheat want to do? Their best response would be Don’t Advertise, which brings expected profits of $4.5 million, better than the expected $4 million from choosing Advertise. If Crunchy Oat chooses Don’t Advertise, what would Sweet Wheat want to do? Their best response is now to Advertise, since their $6 million expected profit is better than the $5 million if they Don’t Advertise. Thus, Sweet Wheat does not have a dominant strategy.
However, we can still predict the outcome of this game. Crunchy Oat does have a dominant strategy and will choose to Advertise. If Sweet Wheat knows that Crunchy Oat will always choose Advertise, they will wisely choose Don’t Advertise. The expected payoffs are $9 million for Crunchy Oat and $4.5 million for Sweet Wheat.
Check that this is, in fact, a Nash equilibrium. Would either firm wish to have made a different choice given the other firm’s strategy? No! Sweet Wheat certainly wishes it could make higher profits but it cannot achieve that unless Crunchy Oat chooses a different strategy. And Crunchy Oat has no incentive to do anything differently.
Is there any incentive for these firms to collude in this example? No. In particular, Crunchy Oat can do no better than the Nash Equilibrium outcome.
- Does Crunchy Oat have a dominant strategy?
- Does Sweet Wheat have a dominant strategy?
- What is the most likely outcome of this game? Is it a Nash Equilibrium?
- Is there a temptation for these firms to collude on strategies? Why / why not?
Answers:
To determine whether Crunchy Oat has a dominant strategy, find their “best response” to each of Sweet Wheat’s strategies. If Sweet Wheat chooses to Advertise, what would Crunchy Oat want to do? They will prefer to Advertise as well (for expected profit of $8 million, which beats the expected profit of $6 million if they don’t Advertise). If Sweet Wheat chooses Don’t Advertise, what would Crunchy Oat want to do? They will still choose to Advertise, since the $9 million expected profit is better than the $7 million from choosing Don’t Advertise. Thus, Crunchy Oat has a dominant strategy: Advertise.
Does Sweet Wheat have a dominant strategy? If Crunchy Oat chooses to Advertise, what would Sweet Wheat want to do? Their best response would be Don’t Advertise, which brings expected profits of $4.5 million, better than the expected $4 million from choosing Advertise. If Crunchy Oat chooses Don’t Advertise, what would Sweet Wheat want to do? Their best response is now to Advertise, since their $6 million expected profit is better than the $5 million if they Don’t Advertise. Thus, Sweet Wheat does not have a dominant strategy.
However, we can still predict the outcome of this game. Crunchy Oat does have a dominant strategy and will choose to Advertise. If Sweet Wheat knows that Crunchy Oat will always choose Advertise, they will wisely choose Don’t Advertise. The expected payoffs are $9 million for Crunchy Oat and $4.5 million for Sweet Wheat.
Check that this is, in fact, a Nash equilibrium. Would either firm wish to have made a different choice given the other firm’s strategy? No! Sweet Wheat certainly wishes it could make higher profits but it cannot achieve that unless Crunchy Oat chooses a different strategy. And Crunchy Oat has no incentive to do anything differently.
Is there any incentive for these firms to collude in this example? No. In particular, Crunchy Oat can do no better than the Nash Equilibrium outcome.
Want to see these concepts demonstrated step-by-step? The videos below cover monopolistic competition and oligopoly.