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12. Imperfect Competition In this chapter you will learn: Differentiated versus homogeneous products;

Forms of competition where firms produce distinctly different products; Monopolistic competition; Hamburger wars; Oligopoly and games; Computer wars; Sequential games; Repeated games; Complex strategies.

12.1 Introduction So far we have studied two extreme cases of market structure, competition and monopoly. Under competition there is a large number of firms, the product being produced is relatively homogeneous, and information flows across the market pretty quickly. The market price is thus determined by the interaction of all of the participants in the market and no single market participant has any market power. Under monopoly, there is only one firm, the monopolist. So the monopolist faces the market demand curve, and, in a sense, has the ultimate amount of market power. However, as we have seen, the monopolist will not pick any price-quantity pair. There is only one price-quantity pair that will maximize profit.

Sometimes we can use the model of competition in cases where it is not immediately obvious the model applies and the model will make predictions that are correct. For example, if Toyota introduces a hybrid car and demonstrates that there is a market for the car, the model of competition predicts that this will create profits and other car companies will also produce a version of a hybrid to compete for those profits. The same is true of the model of the monopolist. For example, the airline industry is not a monopoly or cartel per se. However, if American Airlines raises its ticket price, we can use the monopoly model to predict it will not lose all of its sales.

However, there are markets where there seem to be a large number of participants yet each firm also seems to face a downward sloping demand curve, e.g., the fast food industry. And there are other markets where there are only a small number of firms, each of whom appears to have significant market power, e.g., the jet aircraft industry. Firms also compete over time and develop strategies against their rivals that play out over time. Developing a model that can handle this type of interaction is important in understanding how these markets function. This suggests that perhaps we need to extend our analysis to cover these types of markets as well.

12.2 Monopolistic Competition: The Short Run First, consider a market where there is a large number (8?) of companies competing with one another. However, we will assume the product is differentiated so consumers can tell the difference between one firm's output and another firm's. Product differentiation will imply that each firm faces its own demand curve. In turn, this means that each firm has a small amount of market power. If the firm believes that it faces its own downward sloping demand curve, then when it raises its price, it won't lose all of its customers, only some. Why? Because some of its customers will have "brand loyalty;" some consumers simply like the firm's product better than the competition's product. For example, some people like the way Wendy's cooks a

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hamburger rather than McDonald's. Wendy's can raise their price a bit and not lose such a customer. Of course, at some point they will lose even a loyal customer if they continue raising their price.

Monopolistic competition, as the name suggests, combines elements of both competition and monopoly. There is competition because there are firms producing a close substitute for the firm's own product. There is some monopoly because of brand loyalty, e.g., some people like Coke more than Pepsi, some like their iPhone and not Samsung’s.

If the firm believes that it faces its own downward sloping demand curve, then it will also confront a marginal revenue curve and the cost structure. So its pricing problem will be very similar to the pricing problem faced by the monopolist. To maximize profit the firm will always choose its output where MR = MC. Then we proceed up to the demand curve to figure out what price the firm should charge. Finally, we have to calculate whether the firm is making a profit or not.

In the diagram, the firm chooses its output where MR = MC at point A. The firm determines its price from the demand curve. If it wants to sell y*, it can charge p* at point B. Finally to calculate economic profit, compare p* with the average cost of producing y*. Apparently, p* > AC so the firm is earning an economic profit. This is the gap between B and C.

This is the firm's short run pricing-output decision. It is the best the firm can do. Of course, if the firm does have a differentiated product, then there are several other aspects of competing with other firms that we need to keep in mind. First, advertising plays a much more important role in monopolistic competition than it does in competition. In competition advertising is based solely on providing potential customers with information and its usually information mainly about price. In a market with differentiated products, the advertising has to inform customers about the characteristics of the product that make it unique. So the advertising has to become more persuasive. And this becomes more costly.

Second, product development and innovation becomes much more important. Customers

need to be convinced that the firm's product is "better" in some sense than the competition's product. The competition has a strong incentive to improve its product to capture more of the market. So each firm has a strong incentive to improve its product line. The advertising and development costs are embodied in the cost structure of the firm.

12.3 The Long Run

d

y

p, MR, cost

MR

MC

y*

A

p* BAC

AC •C•

•

3

In the short run a firm may earn an economic profit. However, that success will breed its own demise in a sense because we would expect entry to occur. As entry occurs there will be a tremendous amount of competition. The greater the economic profits, the more competitive the market will become. This is the period where unusual things may happen that are impossible for any model to predict. Some firms will innovate, others will not. Some will advertise effectively, some will not. What is sure is that the consumer will benefit from new products and low prices.

As firms enter the market and compete with one another, the incumbent or original firm will begin to lose control over its own market. In the diagram below the firm starts as a monopolist for its particular product line, perhaps because of a patent, for example. Then one firm comes up with its own design and patent and is able to compete so they enter the market. The original firm's demand curve will shift in and become flatter. Why? Because the original firm begins to lose control over its market as new firms with close substitutes for its product enter the market. A given price increase, say 10%, will cause the original firm to lose more customers when there are close substitutes for its product than when it is a monopolist.

The demand for the original firm's product when it is alone in the market is denoted d0 below. When one firm enters the market, the original firm's demand curve shifts in to d1 and becomes flatter. The flatter the demand curve, the less control the individual firm has. Why? Because when the demand curve is flat, a small price increase will cause it to lose a lot of customers. When the demand curve is very inelastic, the same small price increase will only cause it to lose a few customers. Similarly, when there are two competitors, the firm loses more control over its market and its demand curve shifts in to d2 and becomes even flatter, and so on when there are three competitors, four, five, and more. In the limit under competition, the firm has no market power and believes it faces a perfectly elastic demand curve (even though the market demand may be downward sloping).

Consider a firm that survives competition and the "shakeout" process where weak firms are

eliminated. In equilibrium there must be zero economic profits. Consider the firm depicted below. It begins with a demand curve d0 and it has no competition. Then over time, because of entry, its demand shifts in and becomes less steep to d in the new long run equilibrium. Again the firm maximizes profit by choosing output where MR = MC to yield y*. Price is chosen from the new demand curve d, p*. In equilibrium there must be no economic profit so the average cost curve must be tangent to the demand curve at that price so that p* = AC at y*. If this is true of other participants, then the industry will be in equilibrium.

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However, keep in mind that just because there are no economic profits being made in equilibrium, that doesn't mean a firm in this type of market can become complacent. It must continue to innovate and advertise those innovations to its potential customers. If it doesn't, other firms will take market share away from it. There are numerous cases of this happening. For example, Sears was the largest retailer nationwide, and probably, worldwide as well, in the 1950s and 1960s. Then competition from other retailers like Kmart in the 1970s started to take some of its business. They responded by closer older stores, some of which were in bad neighborhoods, and opening new locations in shopping malls. As another example, in 2010 J C Penny’s came under attack from other retailers and began losing market share rapidly.

12.4 Example: Hamburger Wars. The fast food industry is widely thought to be a perfect example of monopolist competition since its product is differentiated and its advertising is persuasive in nature. There was a large increase in the demand for fast food during the late 1970s and 1980's and the industry expanded dramatically. However, the growth of the industry slowed down considerably in the 1990's. In 1989 industry sales were $56b in the USA and McDonald's was the industry leader. Indeed, McDonald's is the largest provider of meals in restaurants in the world even today.

In the following table we have depicted the sales per franchise of the major fast food companies when the industry had settled down into an equilibrium. McDonald's had sales of $18b in 1989, 10577 outlets worldwide, 8014 outlets in the USA. Sales of the next largest firm, Burger King, were only $5.8b.1

1 Why was McDonald's so successful? 1. Careful selection of franchises. Of the 20,000 plus applicants each year only 150 are chosen and sent to a training school for two years where they learn how to run a franchise. And they must invest at least $66,000 of their own money. 2. Careful site selection. McDonald's studies satellite photos of traffic patterns. 3. Strict standards are set by the main company. They choose the architecture of the restaurant, menu items, new products, prices, and so on. 4. Generous support from the parent company, mainly in advertising. 5. Continuous improvement. Examples : drive through window, an improved drive through window, new products like the egg McMuffin and packaged salads, happy meals for kids, diaper changing stations in the rest rooms, dimmed lights at supper time.

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The competition among the American companies spilled overseas. In 1986, approximately 20% of McDonald's sales came from abroad. In 1990 it was 38%. The American market is pretty much saturated. So other firms are also moving abroad. Wendy's and Burger King are also opening up franchises in other countries in Asia and Europe.

This strongly suggests that in the United States, the fast food industry approached an equilibrium where economic profits were practically zero by the mid 1990s. However, firms cannot remain complacent. They must continue to innovate because if one company doesn't, others will, and that company won't survive. In 1996, a major price war broke out in the industry and McDonald's lost some of its market share. Some of its new products have fizzled with consumers and some of its older franchises are in run down neighborhoods experiencing declining sales. Burger King and Wendy's have both increased their share of the market as a result in the late 1990s. In the early 2000s several new competitors like Subway, Quiznos, and Jimmy Johns entered the market and began competing with the older companies. And some companies are expanding into China and India. However, profits seem to be settling down once again suggesting the industry is back in equilibrium in the 2010s.

Table: Annual sales per franchise (1990) McDonald's $1.6m Burger King $984k Hardee's $920 Jack in the Box $900 Wendy's $759 Arby's $610 Kentucky Fried Chicken $597 Taco Bell $589 Pizza Hut $520 Domino's $485 One of the most important innovations in the fast food industry is supersizing. Wendy’s

discovered that it could increase portion sizes at a fraction of the cost. This caught on and supersizing became common. A study was done tracking the portion size of 181 food products over a forty year period, e.g., candy bars, pizza slices, French fries. The researchers tracked changes in portion size as larger sizes were added to the product line, e.g., bigger candy bars. The following chart is suggestive that the phenomenon is not just associated with the fast food industry. Coincidentally, obesity rates among all age groups started increasing in the late 1970s and have continued increasing since. As of 2009, 30% of the US population is obese. Now the problem appears to have also spread to Europe and even Japan as obesity rates have started rising there as well.

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12.5 Oligopoly: More on Games In Oligopoly there are only a few firms, say two or three. Or there might be two or three large firms that dominate the market and several smaller firms that are able to compete. In such a market it is sometimes easier to use Game Theory to model the type of strategic decision making firms undertake.

For a one shot game, a game played once, there are two ways of representing behavior. The first uses a payoff matrix and is sometimes referred to as the strategic form of the game. Suppose there are two players, A and B. The payoff matrix will take the following form,

Player A is on the left hand side and chooses a row. B is on top and chooses a column. Each

player in the game has several actions she can take and they need not be the same actions. Typically, we list strategies the player can follow rather than actions. However, if the game is played only once strategies coincide with actions. Payoffs are listed in each box of the matrix as an ordered pair, A's profit or payoff first, B's profit or payoff second. Each player chooses an action based on his expectation of what the other player will do.

There is an alternative format for a game called the extensive form and this involves a game tree. This is also a popular method of analyzing situations of uncertainty.

In the following game there are three nodes labeled 1, 2, and 3. A single player moves at a node. For example, player A would move at node 1. Player B would move if the game were at node 2 or 3. The payoffs are listed as ordered pairs at the far right. They coincide with the strategic form of the game.

0

10

20

30

40

50

60

70

number of large

sized portions

introduced

1970-74 1975-79 1980-84 1985-89 1990-94 1995-99

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Extensive form games can be used to represent one shot games or sequential games. For a

one shot game, the two players move simultaneously and the game is played once. In order to model this we have to be careful about the information Player B has when it is her turn to move. This leads to the concept of an information set. If two or more nodes are in an information set, the player does not know which node she is at. If there is only one node in an information set, then she knows the exact node she is at. We use a dashed line to denote an information set. In the diagram below, node 1 is in an information set by itself so A knows he is at node 1 when he moves. Nodes 2 and 3 are in the same information set for B so B does not know whether she is at 2 or 3. This framework can be used to model a simultaneous move game. On the other hand if nodes 2 and 3 are in separate information sets, then B knows exactly where she is at, either node 2 or 3. This can be used to model sequential games where A moves first followed by B. Why? Because in a sequential game, one player moves first by, say, choosing price. Then the other player moves second and chooses her price after observing the first player's choice. However, the first player knows this and will take this into account when making her choice. She may choose a completely different action if she knows the other player will observe it before making his choice than she would if she knew he wouldn't observe it. An equilibrium is a situation where neither player wishes to change his/her action. In order to decide whether a set of actions or strategies is an equilibrium set of decisions, we have to check other possibilities to see if each player can do better for themselves or not.

In the following diagram the player A starts knowing he is at node 1. He moves and then

player B moves. But B knows whether she is at node 2 or at node 3 since each is in a separate information set. This is how we can model a game involving sequential moves. In this case A moves first and B observes how A moved.

•

•

•

nodes

A

B

B

1

2

3

π , πA B

•

•

•A

B

B

1

2

3

π , πA B

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In the following situation B knows whether she is at node 2 or node 3 when she makes her

move. But after she moves A does not know if he is at 4 or 5, or 6 or 7. A remembers whether he moved from 1 to 2 or from 1 to 3 but does not observe B’s move and so doesn’t know where he is inside the information sets. If he moved from 1 to 2, for example, he doesn’t see B’s move after that and so doesn’t know if he is at 4 or 5. Although, he knows he is not at 6 or 7 since he knows he moved from 1 to 2.

Finally, in the following set up, A forgets how he moved at node 1 when it is his chance to

move a second time. Can you figure out why I say that he forgets his first move?

12.6 Computer Wars Consider two computer firms A and B. Each firm can choose to develop a large CPU machine or a small CPU machine. The payoffs are listed in the table below.

1

2

3

A

B

B

1

2

3

A

B

B

4

5

6

7

1

2

3

A

B

B

4

5

6

7

9

Suppose the game is played once. Are there any equilibria? It turns out there are two :

(Small, Large) and (Large, Small). The payoffs are (9, 3) and (12, 5), respectively. Check this : If A thinks B will choose Small, what should A do? Choose Large. If B thinks A will choose Large, what should B do? Choose Small. So (Large, Small) is an equilibrium. Of course, the equilibrium (Large, Small) yields higher profits than the other equilibrium. Nonetheless, there are two equilibria.

We can also represent the game in the extensive form below. We will obtain the same equilibria as before. A chooses Large or Small and B is unaware of A's choice because nodes 2 and 3 are in the same information set. If B expects A to choose Large, then B should choose Small and vice versa. Many who play this game will choose the equilibrium (12, 5) over the other equilibrium because the payoffs are higher for both firms. There is nothing wrong with that outcome. It is perfectly rational.

Notice something important about the game. The two firms are always better off if they choose not to directly compete with one another. So the firms are rationally choosing not to compete with one another. This is actually quite common in business.

Unfortunately, it can create a problem for the government in deciding whether or not to

investigate two such firms. The government might think the firms have colluded in order to earn supra normal profits by choosing not to compete with one another when in fact the firms have rationally chosen not to compete. The problem is that the government will waste a lot of money investigating the two firms and may very well not uncover any incriminating evidence. Of course, on the other hand, they might find something. The problem for the government is that it will never know whether the two firms have colluded or not unless they investigate. When firms choose not to compete with one another, this makes it harder for the government to make its decision as to whether it should investigate or not.

B

A

Small Large

Small

Large

7, 2 9, 3

12, 5 8, 0

•

•

•A

B

B

1

2

3

Small

Large

Small

Large

Small

Large

7, 2

9, 3

12, 5

8, 0

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12.7 Sequential Games. Suppose A moves first and this is observed by B before B moves. Now, when B moves, she will know whether she is at node 2 or node 3. How will the game be played? We start at the end of the game and work our way back to the beginning. Suppose we are at node 2. What should B do? Choose Large because that maximizes her profit since 3 > 2. In that case, what is A's profit? ΠA = 9. What should B do if she finds herself at node 3 instead? Choose Small since 5 > 0. What is A's profit in that event? ΠA = 12. Now we know what B will do when it is her turn to move. Take a step back to node 1. What will A do? If he chooses Small he knows B will choose Large and A's payoff will be 9. On the other hand if A chooses Large instead, he knows B will choose Small and A's payoff will be 12. So A should choose Large knowing that B will respond properly by choosing Small. Apparently, the only equilibrium is (Large, Small) and the equilibrium payoffs are (12, 5). Again the two firms avoid competing directly.

Next, change the 5 to a 3 and the 3 to a 5, as depicted below, and consider the following.

Notice that the sequential equilibrium is again (Large, Small) and the payoffs are now (12, 3). B is not particularly well off. She could be much better off if somehow she could get A to choose Small instead of Large. Why? Because if A chooses Small, then B can choose Large and increase her profit from 3 to 5.

How can B get A to choose Small? Suppose B "threatens" A in the following way. B says to A, "I'll punish you if you choose Large by also choosing Large and I will compete head to head with you. So you better choose Small." If A believes the threat, then his payoff will only be 8 if he chooses Large because of the threat. However, if A chooses Small and B chooses Large, then A's payoff will be 9, i.e., if A believes the threat and goes along with B, his payoff is higher than if he chooses Large and B punishes him, 9 > 8.

What should A do? If he chooses Large, will B punish him? No because B wants to maximize her payoff. If A chooses Large, what is the best B can do? Choose Small. A knows this and so B's threat is not credible or believable. This is an example of an incredible threat, something that is all too familiar in life and in business.

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•A

B

B

1

2

3

Small

Large

Small

Large

Small

Large

7, 2

9, 3

12, 5

8, 0

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Application: There used to be a K-Mart in the building that now houses Winco over in

Moscow. A number of years ago Wal-Mart announced it was going to open a store in Moscow. Kmart threatened to expand and renovate its store in the Palouse Empire Mall and it even went so far as to rent the empty store right next to it. Wal-Mart called Kmart's bluff and moved into Moscow anyway and Kmart gave up and closed its Moscow store. So Kmart's threat was not credible. (I am indebted to Management Professor Isaac Fox for this example.)

12.8 Repeated Games Finally, we want to develop a model of repeated interaction between two firms. This requires us to discount the payoffs over time. Let β = discount factor so that 0 < β < 1. For example, β = 1/3. Consider a stream of receipts where $1 is received each period into the infinite future. The present value of $1 received each period is

1 + β + β2 + β3 + .................... = 1/(1 - β) For example, if β = 1/3, then the present value of the aforementioned stream is 1/(1 - β) =

1/(1 - 1/3) = 3/2. If $125 is received each period and β = 1/3, then the present value of that stream is $125/(1-β) = $125x3/2 = $187.50.

Consider an output game between two firms that lasts forever, where each firm chooses its output level each period. It can choose high or low and the payoffs are as listed below.

Suppose the game is played just once and moves are simultaneous. The only equilibrium is (High, High) and the payoffs are (2, 2). (Make sure you understand why.)

•

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•A

B

B

1

2

3

Small

Large

Small

Large

Small

Large

7, 2

9, 5

12, 3

8, 0

B

A

Low High

Low

High

10, 10 - 2, 15

15, - 2 2, 2

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Suppose the game is played once each period for periods t = 1, 2, 3, ............. into the infinite future. Each player needs to pick a dynamic strategy to play the game with. A dynamic strategy, or strategy for short, is a rule that tells the player what to do in each move of the game. They can be quite complex since we can condition the choice made now by what we observed on previous moves in the game.

Example: "Always choose high output." Example: "Choose low output in odd periods t = 1, 3, 5, ..... and choose high output in even

periods, t = 2, 4, 6, ....." Of course these might not be wise strategies, but they do tell the player exactly what to do

each period the game is played. How can we figure out what the equilibrium will be? Propose two strategies, one for A and

one for B. Then calculate the payoffs when the two players play their strategies. Finally, ask the question : suppose one player deviates from his strategy. Can he do better? If so, then the proposed strategies cannot be an equilibrium. If you cannot find a strategy that is better for one of the players, then the two proposed strategies constitute an equilibrium.

Example: Let S1 = "always choose high output" and suppose both players play this strategy. Is (S1, S1) an equilibrium? (The first S1 listed in the ordered pair refers to A's strategy, the second refers to B's strategy.

1. Calculate A's payoff if both play S1. πA = 2 + 2β + 2β2 + 2β3 + ........ = 2(1 + β + β2 + ....) = 2/(1 - β). Suppose β = 1/3. Then = 2x3/2 = 3 is A's payoff in the infinitely repeated game. What is B's

payoff? The same as A's, πB = 3 because the game is symmetric. 2. Suppose A unilaterally deviates from S1. The best time to deviate is in the first

move because a deviation later gets discounted. Suppose A chooses low output at t = 1 but then chooses high output for t = 2, 3, 4, ...., and so on. Call this new strategy S*. What is her payoff from this new strategy S* when B plays S1, i.e., what is A's payoff to (S*, S1)? If it is higher for (S*, S1) than it is for (S1, S1), then (S1, S1) cannot be an equilibrium.

πA = - 2 + 2β + 2β2 + 2β3 + ...... = - 2 + 2β( 1 + β + β2 + ......) = - 2+ 2β/(1 - β) = - 2 + 2(1/3)(3/2) = - 2 + 1 = - 1 This is worse than if A stayed with S1. The same is true for B. Therefore, (S1, S1) is an

equilibrium for the infinite horizon game! Neither player can deviate from this strategy and do better in the sense of receiving a higher payoff by deviating from S1.

Example : Let S2 = "always choose low output" Is (S2, S2) an equilibrium? A's payoff is πA = 10/(1 - β) = 15 if β = 1/3. Suppose A deviates on the first move of the game and then goes back to S2. His payoff from deviating is 15 + 10β + 10β2 + 10β3 + ... = 15 + 10β(1 + β + β2 + ...) = 15 + 10β/(1 - β) = 15 + 10(1/3)(3/2) = 15 + 5 = 20. This is larger than the payoff if A plays S2 so A should deviate from S2. Therefore, (S2, S2) cannot be an equilibrium in the infinitely repeated output game.

12.9 Trigger Strategies There are other strategies which lead to other outcomes in the output game. Consider the following so-called "trigger" strategy,

ST = 1.) start by choosing low output at t = 1, i.e., the first period;

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2A.) if the other player chose low output at t-1, last period, then continue to choose low output at time t ≥ 2.

2B.) if the other player chose high output at time t-1, last period, then punish the other player by choosing high output at time t ≥ 2 forever after.

The strategy is called a "trigger" strategy because if the other player cooperates and chooses low output the game continues as it has in the past by each player choosing a low output. However, if one player "cheats" and chooses a high output in one period, then that player gets punished the next period when her opponent observes the cheating behavior and forever after.

Suppose both players play this "trigger" strategy. Is it an equilibrium? To check this, we first calculate A's payoff if both play the trigger strategy, then calculate A's payoff for deviating from ST (or "cheating" on the implicit agreement). A's payoff from playing ST is 10/(1 - β) = 15 if β = 1/3. What happens if A deviates from ST? Suppose A deviates in the first period. Then his payoff is 15 and B's payoff is - 2. What happens next period at time t = 2? B observes A's behavior the previous period and punishes A by always choosing high output from t = 2 on. A's payoff will either be 2 or - 2. If A expects B to punish him, he will choose the action that gets him a payoff of 2, high output. That is where the game will remain for the rest of the game. So A's payoff from deviating is

15 + 2β + 2β2 + 2β3 + .... = 15 + 2β/(1 - β). Is the payoff from ST greater than the payoff obtained when deviating from ST? If 10/(1 - β) ≥ 15 + 2β/(1 - β), or after simplifying, if β ≥ 5/13 = 38.5%, then A should play

part #1 of ST and not cheat or deviate. If β < 5/13, then A should deviate. Example : β = 2/3. πA(play ST) = 10/(1 - β) = 30, and πA(deviate from ST) = 15 +

2(2/3)(3) = 15 + 4 = 19 so stay with ST. Example: β = 1/3. πA(play ST) = 10/(1 - β) = 15, and πA(deviate from ST) = 15 +

2(1/3(3/2) = 15 + 1 = 16 so deviate from ST. What is the intuition behind these results? If no deviation occurs, the payoff is 10 + β10 + β210 + .......... If a deviation occurs on the first move of the game, the payoff is instead 15 + β2 + β22 + ............. What happens if player A doesn't care about the future and β = 0 as a result? Then the

benefit to cheating is positive (15 - 10 = 5) but the cost, as perceived by A, is zero since A doesn't care about the future! So when a player cheats he receives a benefit right away but only pays a cost in the future. The more the player cares about the future, the greater the present value of the cost of cheating and the more likely it will be that he will choose not to cheat.

12.10 Interpretation of the Trigger Strategy Equilibrium The importance of the trigger strategy is that two firms can be playing a trigger strategy and it may look like they are cooperating to create a cartel when in fact they are not. The government may begin to investigate and spend a lot of money and time in doing so. However, the two firms may simply be playing a strategy that implicitly recognizes the gains to be had by being cooperative rather than being too competitive.

The interesting issue is that it is not immediately obvious how one pursues anti-trust policy in light of these examples. Firms certainly look to the future and try to figure out their competitors strategies. Firms may try to avoid direct competition by choosing to segment the market rather than compete head to head. And firms may look like they are behaving cooperatively rather than

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competitively because implicitly the two firms recognize they can do better by not competing directly.

12.11 The Entry Game There are a number of interesting applications of game theory to oligopoly markets. Suppose firm A is an incumbent firm already in the market and B is a potential competitor thinking about entering A's market. Suppose the payoffs are as listed in the table below.

A can resist B's entry by cutting its price and advertising more, or A can choose not to resist B's entry. B can choose either to enter A's market or not.

Suppose A announces that it will strongly resist B's entry into the market. What should B do? B must figure out whether A's threat is real or not. Suppose B enters the market. What will A actually do? Since 3 > 2, A will choose not to resist once B enters. Suppose B chooses not to enter. Then there is nothing to resist so A will choose not to resist (12 > 11). So in either case B should expect that A will not resist. Therefore, B should enter since it expects A not to resist. So B enters, A chooses not to resist, and the result is (do not resist, enter) and the payoffs are (3, 11).

Suppose A can take an action in an effort to convince B that A is serious about resisting B's

entry before B makes its decision. A can build excess capacity in its plants, for example. This might send B a strong signal that A will gear up production and flood the market with its product momentarily driving price down below cost for B. Building a new plant or expanding an existing one is very costly and will lower the payoffs of the table for A. However, extra production may increase profits while resisting. Suppose the new payoffs are listed as below. Now B will expect A to resist. The equilibrium is now (resist entry, do not enter) and the payoffs are (11, 8). A is better off than if it did not build excess capacity although a price was paid in lower profit in having to fight entry into its market.

This instructs us that a firm in an imperfectly competitive market may take actions which

seem strange in the sense that they may lower its profit. However, the action may be a pre-emptive strike, in a sense. For example, a firm may buy a small company that is losing money with little hope of increased sales. Why? To make itself less of a target for a takeover bid from

B

A

Enter !! Do not enter

Resistentry

Do notresistentry

2, 5 11, 8

3, 11 12, 8

B

A

Enter !! Do not enter

Resistentry

Do notresistentry

1, 5 11, 8

1/2, 11 10, 8

15

a larger firm. And many times firms take on what appears to be too much debt for the same reason, to lessen their attraction to another, larger firm that might want to take them over. These actions are designed to alter the payoffs in the payoff matrix in such a way as to alter the opponent's strategy and hence the outcome of the game.

12.12 Sequential Entry Game Suppose B is the incumbent in an industry and another firm, A, is thinking about moving into the market. A moves first, B observes the move, and moves second. The only Nash equilibrium, given the payoffs below is where A enters and B produces normally. B is worse off if A enters. What happens if B threatens A by saying it will flood the market and drive A’s potential profit down if A enters? This is an example of an incredible threat since if A has already entered, the best B can do is produce normally. So the Nash equilibrium is (enter, produce normally). Notice that B loses profit when A enters. It drops from 7 to 4.

Suppose the incumbent B can take an action before A chooses by, say, expanding it’s

operation. This complicates the game considerably. B moves first and can expand or not. If B doesn’t expand the game moves from node 1 to

node 2 and the game is played as before. In that case the Nash equilibrium is the same as before, A enters, B produces normally, and each gets a payoff of 4. If B expands its operation, the game moves from node 1 to 3, and A can choose to enter or not. Finally, if B expands and A enters, then B can choose to flood the market or not.

How will this game be played? We basically work backwards from the end choosing the best action for each player. Suppose the game is at node 2. What should A do? A should enter because he knows that if he enters B will produce normally and A’s profit is 4. So if B is at node

B

enter

don’t enter

flood themarket

producenormally

2, 2

A

3, 7

4, 4

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1 and chooses “don’t expand” what can he expect A to do? Enter, in which case B will produce normally and earn a profit of 4, πB = 4. On the other hand suppose we are at node 4 instead. What should B do? Produce normally where his profit is πB = 2. So if the game is at node 3, what should A do? A should choose “don’t enter” because if he does his profit will be πA = 3, while his profit if he chooses “enter” is only πA = 2. Finally, suppose B is at node 1. If he chooses “don’t expand” he knows A will enter and that he will produce normally and earn πB = 4. On the other hand if he chooses “expand” instead, A will choose “don’t enter” and B’s profit is πB = 5. He should choose expand.

The Nash equilibrium is A = don’t enter, B = expand, and the payoffs are (πA, πB) = (3, 5). Expanding is an example of a pre-emptive strike that alters the payoffs of the game in B’s favor.

12.13 Another Example of a Repeated Game: Cartels Consider the cartel game from chapter 10. There are two firms and the payoff structure is the following. There are two firms and they each can choose either high output or low output. If the game is played just once, a so-called one shot game, the Nash equilibrium is where each chooses a high output and the payoffs are (2, 2). They can try to form a cartel and agree to choose low output. However, each will have a strong incentive to cheat and the cartel will fail; cartels are inherently unstable.

We can ask what happens if the game is repeated. A strategy must inform the player of what

action to take in each play of the game. So strategies generally differ from actions in a repeated

A

B

enter

don’t enter

flood themarket

produce normally

B

expand

don’t expand

B

enter

don’t enter

flood themarket

produce normally

2, 2

A

7, 3

5, 3

1

2

3

4

5

4, 4

1, 1

2, 2

Blow output high output

Alowoutput

highoutput

5, 5!! 1, 7

7, 1 2, 2

17

game. In fact, a strategy is made up of a sequence of actions. And a strategy must inform the player how to choose on each play of the game.

Consider the strategy S1 = "always choose high output" and suppose both players choose S1. Is the pair of strategies (S1, S1), where the fist component is A's choice and the second component of the ordered pair is B's choice, a Nash equilibrium? First, calculate the payoff if both play the strategy and then see if A can increase his payoff by deviating. A's payoff is

2 + 2β + 2β2 + ..... = 2/(1 - β). B's payoff is the same as A's. Now suppose A deviates on the first move and then reverts to

the S1 strategy. His payoff is 1 + 2β + 2β2 + ..... = 1 + 2β/(1 - β). This is less than the payoff from playing S1. If A deviates on the third move his payoff is 2 + 2β + 1β2 + 2β3 + ...... This is also less than when he chooses to stick with S1. Waiting to deviate lowers his payoff

even more since 1 > 1β3. So it doesn't pay for him to deviate. The same is true for B. Therefore, the pair (S1, S1) is a Nash equilibrium. This replicates the Nash equilibrium in the one shot game in each period of the repeated game. We would observe (high, high) in the one shot game and (high, high) in each play of the repeated game.

Is a cartel stable in the repeated game? Let S2 = "alwats choose low output," and suppose both players play this new strategy. Is the pair (S2, S2) a Nash equilibrium? If so, then the cartel agreement is stable. A's payoff is

5 + 5β + 5β2 + ..... = 5/(1 - β). Suppose A deviates on the third move of the game and then reverts to S2 again. His payoff is 5 + 5β + 7β2 + 5β3 + ....... Clearly, this is larger than if A does not deviate so she should deviate. In fact, she should

deviate on the first move of the game, since 7 + 5β + 5β2 + ..... > 5 + 5β + 7β2 + 5β3 + ....... So the cartel is still unstable. Will a more complicated strategy work? Consider the following trigger strategy: ST = 1. Choose low at t = 1; 2a. Choose low at time t > 1 if opponent chose low at t - 1; 2b. Choose high at t > 1 forever if opponent chose high at t - 1. Is (ST, ST) a Nash equilibrium? A's payoff is 5 + 5β + 5β2 + ..... = 5/(1 - β). Both players start with low and continue to choose low as long as the other player chose low

in the previous period. Suppose A deviates on the first move and then reverts back to the trigger strategy. He gets 7 at t = 1. What happens at t = 2? B starts to punish A by choosing high and A reverts to the trigger strategy by choosing low for a payoff of 1. At t = 3 A realizes that B chose high at t = 2 and his trigger kicks in so he also chooses high and gets 2 each period for the rest of the game. His payoff is

7 + 1β + 2β2 + 2β3 + ...... = 7 + 1β + 2β2(1 + β + β2 + β3 + ......) = 7 + 1β + 2β2/(1 - β). Now it is not immediately obvious whether A should deviate or not. Suppose β = 0. Then in comparing the payoffs A should deviate. Why? When he deviates he

gets 7 and 7 > 5. If β = 0, he doesn't care about the future cost when he is punished. However, if the discount factor β increases, and is positive, then he will care about the future cost. Eventually, if β is high enough he will care a lot about the future cost and will choose to stick with the cartel.

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We have the following simple rule: play ST if 5/(1 - β) > 7 + 1β + 2β2/(1 - β). Rearrange the inequality and simplify to get

5 > 7(1 - β) + β(1 - β) + 2β2. 5 > 7 - β7 + β + β2. 5 > 7 - β6 + β2. β6 - β2 > 2. If β6 - β2 > 2, play ST; otherwise deviate. For example, suppose β = 2/3. The rule is 4 - 4/9 >

2, which holds so choose ST and don't deviate. If β = 1/3, the rule becomes 2 -1/9 > 2, which is

12.14 Example: Sugar Substitutes The article, “Showdown at the Coffee Shop,” (NYTimes, 4, 2009) discusses the artificial sweetener industry and the so-called “packet wars” that broke out in the mid 2000s. In the late 1800s the first artificial sweetener was discovered by accident, Saccharin. It grew in popularity during the sugar shortage of World War 1. In 1957 saccharin was sold in pink packets of Sweet N’ Low and became popular among diabetics and those wanting to lose weight.

It wasn’t until Aspartame was developed in the early 1980s that there was any serious competition when blue packets of Equal hit the packet market. The next major source of competition came from sucralose, which found its way into Splenda in 1999. The industry settled into an equilibrium with pink, blue, and yellow packets competing for market share. By 2007 Splenda dominated the market controlling 60% of the market. Now a new entrant has appeared, stevia, backed by the Ag giant Cargill. Stevia, based on neotame, is 13,000 times more sweet than sugar. Apparently, a little goes a long way.

As the obesity epidemic got worse, the demand for these products increased dramatically in the 2000s. Entry suggests there are large economic profits being made in this industry.

12.15 Conclusion There are many markets that do not coincide with the assumptions of our model of perfect competition. In some cases there is a large number of firms but the product they are selling is differentiated; it is literally distinguishable from the product produced by other firms. In other cases there are only a few firms competing with each other, e.g., Apple and Samsung and a few smaller companies in cell phones. Such firms will not behave as perfect competitors would. They will use complex strategies in choosing actions to compete with their rivals. We developed some simple tools using game theory to assess the strategies firms might choose and applied those tools to several examples.

Important Concepts Monopolistic competition short run, long run Game theory strategic form, extensive form One shot games Sequential games Repeated games dynamic strategies, trigger strategies Examples

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the entry game, keeping promises, the advertising game Review Questions 1. What is the difference between monopolistic competition and competition? What is the

difference between monopolistic competition and monopoly? How does the short run differ from the long run equilibrium of a monopolistically competitive industry?

2. What is the strategic form of a game? What is the extensive form for a game? 3. What is a one shot game? How does it differ from a sequential or repeated game? 4. What is a dynamic strategy? What is a trigger strategy? Practice Questions 1. Can economic profits exist in the long run in an industry characterized by monopolistic

competition? a. Yes. b. No. 2. What is the difference between an industry characterized by perfect competition and one

characterized by monopolistic competition? a. There is no difference; they are essentially the same. b. Under perfect competition economic profits can exist in the long run, under monopolistic

competition profits cannot exist. c. Under monopolistic competition economic profits can exist in the long run, under perfect

competition profits cannot exist. d. The product is differentiated under monopolistic competition, it is not under perfect

competition. e. The product is differentiated under perfect competition, it is not under monopolistic

competition. 3. Consider a game between two duopolists over price. Each can choose a high price or a

low price. The payoffs are listed below. What is the equilibrium of the one shot game?

4. Given the payoffs of the last question, suppose the game is played repeatedly over time

and let β be the discount factor. Calculate the payoff for A if both players play the strategy "always choose a high price."

5. Given the payoffs of the last question, can A benefit from deviating from the strategy

"always choose a high price?"

B

A

low price high price

lowprice

highprice

1, 1 5, - 1

- 1, 5 3, 3

20

6. Brad and Angelina are going to produce and sell bobble head dolls of themselves to donate to charity. If they use mark-up pricing and maximize profit, then

a. the mark-up price will be higher the smaller the elasticity of demand. b. the mark-up price will be higher the larger the elasticity of demand. c. the mark-up price will be smaller the smaller the elasticity of demand. d. they are behaving inconsistently because profit maximization is incompatible with mark-

up pricing. e. the mark-up price will be the same as the price under monopolistic competition. 7. What were the two top fast food companies during the 1980's when the industry

dramatically expanded? Pick two from the list below a. Burger King. b. Wendy's c. Pizza Hut d. Wal-Mart e. MacDonald's 8. Taco Bell lost a large lawsuit brought by its own employees because Taco Bell refused to

pay over time and forced many workers to work "off the clock" (without pay). Taco Bell will not be allowed to force workers to work off the clock and will have to pay over time. What will this do to its cost structure?

dy

p, MR, cost

MR

MC

y*

ACp*

a. It will cause it to shift upward. b. It will cause it to shift downward. c. It will cause it to shift horizontally to the left. d. It will not affect it. 9. Given the information of the last question, how will the legal settlement affect Taco

Bell's profitability? a. It will not affect it at all. b. Since costs have increased, the economic profit it was earning will be wiped out. c. Since costs have decreased, the economic profit it was earning will be increased. d. Since costs have simply shifted horizontally to the left, the economic profit it was earning

will not be affected.

21

e. Since its economic profit was zero to begin with and costs have increased, it will be earning negative economic profits after the settlement.

Answers 1. b. 2. d. 3. The set of strategies (low, low) is the only equilibrium in the one shot game. 4. The payoff to both players is 3/(1 - β). 5. Yes, because the payoff from deviating is 5 + 3β/(1 - β) and this is greater than 3/(1 - β). 6. a. 7. a, e 8. a. 9. e.