Take home assignments

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1 Game Theory and Business Strategy Take home assignments Chapter 12 Exercise 2.1 Exercise 2.3 Exercise 2.7 Exercise 2.8 Exercise 4.1 Exercise 5.3 Chapter 13 Exercise 1.4 Exercise 2.3 Exercise 2.6 Exercise 3.2 Exercise 4.1 Exercise 5.3 Exercise 6.2 1

2 Recall the Cournot duopoly with American and United. Oligopoly Games Looking at the same market from a game theory perspective Players and Rules Two players, American and United, play a static game (only once) to decide how many passengers per quarter to fly. Their objective is to maximize profit. Rules: Other than announcing their output levels simultaneously, firms cannot communicate (no side-deals or coordination allowed). Complete information Strategies Each firm s strategy is to take one of the two actions, choosing either a low output (48 k passengers per quarter) or a high output (64 k). 2

3 Payoff Matrix or Profit Matrix Both firms know all strategies and corresponding payoffs for each firm. The Table summarizes this information. For instance, if American chooses high output (q A =64) and United low output (q U =48), American s profit is $5.1 million and United s $3.8 million. Dominant Strategies If available, a rational player always uses a dominant strategy: a strategy that produces a higher payoff than any other strategy the player can use no matter what its rivals do. 3

4 Dominant Strategies Dominant Strategy for American If United chooses the high-output strategy (q U = 64), American s highoutput strategy maximizes its profit. If United chooses the low-output strategy (q U = 48), American s highoutput strategy maximizes its profit. Thus, the high-output strategy is American s dominant strategy. Dominant Strategies Dominant Strategy Solution Similarly, United s high-output strategy is also a dominant strategy. Because the high-output strategy is a dominant strategy for both firms, we can predict the dominant strategy solution of this game is q A = q U = 64. 4

5 Dominant Strategy Solution Dominant Strategy Solution is not the Best Solution A striking feature of this game is that the players choose strategies that do not maximize their joint or combined profit. In the Table, each firm could earn $4.6 million if each chose low output (q A = q U = 48) rather than the $4.1 million they actually earn by setting q A = q U = 64. Prisoner s Dilemma Game Prisoners dilemma game: all players have dominant strategies that lead to a payoff that is inferior to what they could achieve if they cooperated. Given that the players must act independently and simultaneously in this static game, their individual incentives cause them to choose strategies that do not maximize their joint profits. Nash Equilibrium Best Responses Best response: the strategy that maximizes a player s payoff given its beliefs about its rivals strategies. A dominant strategy is a strategy that is a best response to all possible strategies that a rival might use. In the absence of a dominant strategy, each firm can determine its best response to each of the possible strategies chosen by its rivals. Strategy and Nash Equilibrium A set of strategies is a Nash equilibrium if, when all other players use these strategies, no player can obtain a higher payoff by choosing a different strategy. A Nash equilibrium is self-enforcing: no player wants to follow a different strategy. Finding a Nash Equilibrium 1 st : determine each firm s best response to any given strategy of the other firm. 2 nd : check whether there are any pairs of strategies (a cell in profit table) that are best responses for both firms, so the strategies are a Nash equilibrium in the cell. (each dominant strategies equilibrium is also a Nash equilibrium but not viceversa. Why?) 5

6 Nash Equilibrium A More Complicated Game Now American and United can choose from 3 strategies: 96, 64, or 48 passengers. Same rules as before: static simultaneous game, perfect information. Nash Equilibrium A More Complicated Game Now American and United can choose from 3 strategies: 96, 64, or 48 passengers. Same rules as before: static simultaneous game, perfect information. 6

7 Best response First: Best Responses If United chooses q U = 96, American s best response is q A = 48; if q U = 64 American s best response is q A = 64; and if q U = 48, q A = 64. (all dark green) If American chooses q A = 96, United s best response is q U = 48; if q A = 64, United s best response is q U = 64; and if q A = 48, q U = 64. (all light green) Best response Second: Nash Equilibrium In only one cell are both the upper and lower triangles green: q A = q U = 64. This is a Nash Equilibrium: neither firm wants to deviate from its strategy. But, equilibrium does not maximize joint profits. 7

8 Types of Nash Equilibria Unique Nash Equilibrium Unique Nash equilibrium: only one combination of strategies is each firm s strategy a best response to its rival s strategy. Examples: Bertrand and Cournot models, all games played so far. Multiple Nash Equilibria Many oligopoly games have more than one Nash equilibrium. To predict the likely outcome of multiple equilibria we may use additional criteria. Mixed Strategy Nash Equilibria In the games we played so far, players were certain about what action to take (pure strategy). When players are not certain they use a mixed strategy: a rule telling the player how to randomly choose among possible pure strategies. Multiple Nash Equilibria Multiple Nash Equilibria Many oligopoly games have more than one Nash equilibrium. To predict the likely outcome of a game we may use additional criteria. Multiple Equilibria Application Coordination Game (TV Network): Two firms firm chooses simultaneously & independently to schedule a show on Wed or Thu. If firms schedule it on different days, both earn 10. Otherwise, each loses 10. 8

9 Multiple Nash Equilibria Best Responses Neither network has a dominant strategy. For each network, its best choice depends on the choice of its rival. If Network 1 opts for Wed, then Network 2 prefers Thu, but if Network 1 chooses Thu, then Network 2 prefers Wed. Multiple Nash Equilibria Two Nash Equilibrium Solutions The Nash equilibria are the two cells with both firms best responses (green cells) These Nash equilibria have one firm broadcast on Wed and the other on Thu. We predict the networks would schedule shows on different nights. But, we have no basis for forecasting which night each network will choose. 9

10 Multiple Nash Equilibria Cheap Talk to Coordinate Which Nash Equilibrium Firms can engage in credible cheap talk if they communicate before the game and both have an incentive to be truthful (higher profits from coordination). If Network 1 announces in advance that it will broadcast on Wed, Network 2 will choose Thu and both networks will benefit. The game becomes a coordination game. Pareto Criterion to Coordinate Which Nash Equilibria If cheap talk is not allowed or is not credible, it may be that one of the Nash equilibria provides a higher payoff to all players than the other Nash equilibria. If so, we expect firms acting independently to select a solution that is better for all parties (Pareto Criterion), even without communicating. Mixed Strategy Nash Equilibria Static Design Competition Game: Two firms compete for an architectural contract and simultaneously decide if their proposed designs are traditional or modern. If both firms adopt the same design then the established firm (E) wins. However, if the firms adopt different designs, the upstart (U) wins the contract. U s best response: modern design if E uses a traditional design, and traditional design if E picks modern. E s best response: modern design if U uses a modern design, and a traditional design if U picks traditional. 10

11 Mixed Strategy Nash Equilibria Pure Strategies No Nash Equilibrium Given the best responses, no cell in the table have both triangles green. For each cell, one firm or the other regrets their design choices. Thus, if both firms use pure strategies, this game has no Nash equilibrium. Mixed Strategy Nash Equilibria Mixed Strategy and Nash Equilibrium However, if each firm chooses a traditional design with probability ½, this design game has a mixed-strategy Nash equilibrium. The probability that a firm chooses a given style is ½ and the probability that both firms choose the same cell is ¼. Each of the four cells in the is equally likely to be chosen with probability ¼. The established firm s expected profit the firm s profit in each possible outcome times the probability of that outcome is 9, the highest possible. The firm just flips a coin to chose between its two possible actions. Similarly, the upstart s expected profit is 9 and flips a coin too. Why would each firm use a mixed strategy of ½? Because it is in their best interest to flip a coin. If U knows that E will choose traditional design with probability > ½ or 1, then the upstart picks modern for certain and wins the contract. So, it is best for E to flip a coin (probability = ½). 11

12 Mixed Strategy Nash Equilibria Each firm maximizes its expected profit. Consider U s choice between the two actions if it knows that the probability that E chooses the traditional style is θ E. U s expected payoff is Eπ U (Traditional) = θ E * (-2) + (1 - θ E ) * 20 = θ E Eπ U (Modern) = θ E * 20 + (1 - θ E ) * (-2) = θ E How to choose: when θ E < ½, Eπ U (trad) > Eπ U (modern) choose Traditional when θ E > ½, Eπ U (trad) < Eπ U (modern) choose Modern when θ E = ½, Eπ U (trad) = Eπ U (modern) indifferent, any random choice between the two pure strategies gives the same payoff choose any θ U between 0 and 1 Mixed Strategy Nash Equilibria E is in the same position. Therefore, if each firm picks a probability of 1/2, the result is a Nash equilibrium. Each firm is doing the best it can given its rival s strategy. For example, if θ E were greater than 1/2, U would pick the modern style and would win most (θ E ) of the time. Similarly, if θ E were lower than ½. Therefore, E would not be happy with its choice, so θ E 1/2 is inconsistent with a mixed-strategy Nash equilibrium. Remember: θ E is the probability the Established firm chooses Traditional θ U 1 ½ θ U (θ E ) ½ θ E (θ U ) 1 θ E 12

13 Information & Rationality Incomplete Information We have assumed so far firms have complete information: know all strategies and payoffs. However, in more complex games firms have incomplete information. Incomplete information may occur because of private information or high transaction costs. Bounded Rationality We have assumed so far players act rationally: they use all their available information to determine their best strategies (maximizing payoff strategies). However, players may have limited powers of calculation, or be unable to determine their best strategies (bounded rationality). Equilibrium, Incomplete & Bounded Rationality When firms have incomplete information or bounded rationality, the Nash equilibria is different from games with full information and rationality. Static Investment Game Static Investment Game Google and Samsung must decide to invest or do not invest in complementary products that go together. (Chrome OS and Chromebook, respectively) There is a payoff asymmetry: A Chromebook with no Chrome OS has no value at all, but Chrome OS with no Chromebook still has value. 13

14 Static Investment Game Nash Equilibrium with Complete Information If each firm has full information (payoff matrix in the Table), Google s dominant strategy is to invest and Samsung s best response to it is to invest. The solution is a unique Nash Equilbrium with both firms investing. Static Investment Game Nash Equilibrium with Incomplete Information If payoffs are not common knowledge, then Samsung does not know Google s dominant strategy is always to invest. Given its limited information, Samsung weights a modest gain versus a big loss. If it thinks it is likely Google will not invest (big loss), then Samsung does not invest. 14

15 Information & Rationality Rationality: Bounded Rationality We normally assume that rational players consistently choose actions that are in their best interests given the information they have. They are able to choose payoff-maximizing strategies. However, actual games are more complex. Managers with limited powers of calculation or logical inference (bounded rationality) try to maximize profits but, due to their cognitive limitations, do not always succeed. Rationality: Maximin Strategies In very complex games, a manager with bounded rationality may use a rule of thumb approach, perhaps using a rule that has worked in the past. A maximin strategy maximizes the minimum payoff. This approach ensures the best possible payoff if your rival takes the action that is worst for you. The maximin solution for the innovation game is for Google to invest and for Samsung not to invest. Bargaining Bargaining Situations - Bargaining is important in our personal lives. - Bargaining is also common in business situations. Managers and employees bargain over wages and working conditions, firms bargain downstream with suppliers and bargain upstream with distributors. Bargaining Games Bargaining game: any situation in which two or more parties with different interests or objectives negotiate voluntarily over the terms of some interaction, such as the transfer of a good from one party to another. For simplicity we will focus on two-person bargaining games Bargaining Game Solution The solution for bargaining games is called Nash Bargaining Solution. Nash Bargaining solution Nash Equilibrium. The Nash Equilibrium is for non-cooperative games where players do not negotiate quantities or prices. 15

16 The Nash Bargaining Solution The Nash bargaining solution to a cooperative game is efficient in the sense that there is no alternative outcome that would be better for both parties or strictly better for one party and no worse for the other. The game American vs. United becomes a bargaining game if rules allow firms to bargain over their output levels and reach a binding agreement. Finding a Nash Bargaining Solution 1 st, find the profit at the disagreement point: the outcome that arises if no agreement is reached, call it d. d A = d U = nd, if a proposed agreement is reached, the firm earns a profit of π and a net surplus, π d. π A d A and π U d U 3 rd, the Nash bargaining solution is the outcome in which each firm receives a non-negative surplus and in which the product of the net surplus of the two firms (called the Nash product, NP) is maximized. NP = (π A d A ) x (π U d U ) 16

17 Airline Game Nash Bargaining Solution To maximize NP = (π A d A ) x (π U d U ), there are 4 possible outcomes. In the upper left cell, in which each firm produces the large output, the NP = 0 because each firm has zero net surplus. In the lower left cell and in the upper right cell, NP < 0. In the lower right cell, where each firm produces the small output and earns 4.6, NP = ( ) ( ) = 0.25, maximum NP. So, the Nash Bargaining Equilibrium predicts both American and United fly 48 thousand passengers. Bargaining and Collaboration Allowed? If the firms could bargain about how they set their output levels in an oligopoly game, they could reach an efficient outcome that maximizes the Nash product. Such an agreement creates a cartel and raises the firms profits. The gain to firms from such a cartel agreement is more than offset by lost surplus for consumers (Chapter 11). Consequently, such agreements are illegal in most developed countries under antitrust or competition laws. 17

18 Nash bargaining more in details Assume two players bargain over how to split a pie of size 1 Player 1 gets x and player 2 gets 1 x How can we predict the result of their interaction? In other words, what is the likely outcome of an efficient negotiation? Nash bargaining more in details Make use of the following notation d 1 is the payoff of player 1 in case of a breakdown of the negotiation and d 2 is the payoff of player 2 in case of a breakdown of the negotiation b is the (exogenous) bargaining power of player 1 1 b is the (exogenous) bargaining power of player 2 Find the value of x which maximises the Nash product Max x (x d 1 ) b (1 x d 2 ) 1-b Solution is x* = b + d 1 (1 b) - d 2 b More intuitively, when b = ½ x* = ½ + ½ d 1 ½ d 2 18

19 Nash bargaining more in details Nash product when b= ½ and d1=d2 Optimal a split of the pie Nash bargaining more in details Nash product when b= ½ and d1=0.3 and d2=0.1 A higher disagreement payoff is favourable to player 1 19

20 Nash bargaining more in details Nash product when b= 0.3 and d1=d2=0 A stronger bargaining power of player 2 is is favourable to him/her Auctions Auction Games Auction: a sale in which a good or service is sold to the highest bidder. In auction games, players called bidders devise bidding strategies without knowing other players payoff functions. A bidder needs to know the rules of the game: the number of units being sold, the format of the bidding, and the value that potential bidders place on the good. Real Scenarios for Auction Games Government related games: Government procurement auctions; auctions for electricity and transport markets; auctions to concede portions of the airwaves for radio stations, mobile phones, and wireless internet access. Market transaction games: goods commonly sold at auction are natural resources such as timber and drilling rights for oil, as well as houses, cars, agricultural produce, horses, antiques, and art. And of course, goods online in sites like ebay. 20

21 Elements of Auctions Number of Units - Auctions can be used to sell one or many units of a good. Format of Bidding English auction: Ascending-bid auction process where the good is sold to the last bidder for the highest bid. Common to sell art and antiques. Dutch auction: Descending-bid auction process where the seller reduces the price until someone accepts the offered price and buys at that price. Sealed-bid auction: Bidders submit a bid simultaneously without seeing anyone else s bid and the highest bidder wins. In a first-price auction, the winner pays its own, highest bid. In a second-price auction, the winner pays the amount bid by the second-highest bidder. Value Private value: Individual bidders know how much the good is worth to them but not how much other bidders value it. Common value: The good has the same value to everyone, but no bidder knows exactly what that value is. In a timber land auction, bidders know the price of lumber but not how much lumber is in the trees. Bidding Strategies in Private- Value Auctions Second Price Auction Second-Price Auction Game Rules: traditional sealed-bid, second-price auction. Each bidder places a different private value on a single, indivisible good. The amount that you bid affects whether you win, but it does not affect how much you pay if you win, which equals the second-highest bid. Second-Price Auction Best Strategy Bidding your highest value is your best strategy (weakly dominates all others). Suppose that you value a folk art carving at $100. If you bid $100 and win, your CS = nd price. If you bid less than $100, you risk not winning. If you bid more than $100, you risk ending up with a negative CS. So, bidding $100 leaves you as well off as, or better off than, bidding any other value. 21

22 Bidding Strategies in Private- Value Auctions English Auction English Auction Game Rules: Ascending-bid auction process where the good is sold to the last bidder for the highest bid. Each bidder has a private value for a single, indivisible good. The amount that you bid affects whether you win and pay. English Auction Best Strategy Your best strategy is to raise the current highest bid as long as your bid is less than the value you place on the good. Suppose that you value a folk art carving at $100. If you bid an amount b and win, your surplus is $100 b. Your surplus is positive or zero for b 100. But, negative if b > 100. So, it is best to raise bids up to $100 and stop there. If all participants bid up to their value, the winner will pay slightly more than the value of the second-highest bidder. Thus, the outcome is essentially the same as in the sealed-bid, second-price auction. Bidding Strategies in Private- Value Auctions Dutch and First-Price Sealed Bid Auction Dutch Rules: Descending-bid auction process where the seller reduces the price until someone accepts the offered price and buys at that price. Sealed Bid Rules: Bidders submit a bid simultaneously without seeing anyone else s bid, the highest bidder wins and pays its own bid. In both games, each bidder has a private value for a single, indivisible good. The amount that you bid affects whether you win and pay. Best Strategies and Equivalence of Outcomes The best strategy for both games is to bid an amount that is equal to or slightly greater than what you expect will be the second-highest bid, given that your value is the highest. Bidders shave their bids to less than their value to balance the effect of decreasing the probability of winning and increasing CS. The bid depends on the beliefs about the strategies of rivals. Thus, the expected outcome is the same under each format for privatevalue auctions: The winner is the person with the highest value, and the winner pays roughly the second-highest value. 22

23 The winner s curse occurs in common-value auctions The winner s curse occurs in common-value auctions: the winner s bid exceeds the common-value item s value. So, the winner ends up paying too much. The overbidding occurs when there is uncertainty about the true value of the good, as is in timber land auctions. Best Strategy to Avoid the Winner s Curse Rational bidders shade or reduce their bids below their estimates. The amount of reduction depends on the number of other bidders, because the more bidders, the more likely that the winning bid is an overestimate. Bounded Rationality and the Winner s Curse Although rational managers should avoid the winner s curve, there is strong empirical evidence for the winner s curse (corporate acquisition market). One explanation is bounded rationality. Collusion in auctions Consider the 1999 German sale of ten blocks of spectrum Multi-unit simultaneous ascending auction: several objects are sold at the same time, with the price rising on each of them independently, and none of the objects is finally sold until no-one wishes to bid again on any of the objects. Rule for this specific auction: any new bid on a block had to exceed the previous high bid by at least 10%. Two potential winners: Mannesman and T-Mobil 23

24 Collusion in auctions Mannesman s first bids were million DM per MHz on blocks million DM per MHz on blocks These were low prices, but the only other credible bidder, T-Mobil, bid even less in the first round. T-Mobil s managers said. Mannesman s first bid was a clear offer. Collusion in auctions The point, of course, is that plus a 10% raise equals T-Mobil understood that if it bid 20 million DM per MHz on blocks 1-5, but did not bid again on blocks 6-10, the two companies would then live and let live with neither company challenging the other on the other s half. Exactly that happened. So the auction closed after just two rounds with each of the bidders acquiring half the blocks for the same low price 24

25 Collusion in auctions Multi-license U.S. spectrum auction Two players: U.S. West, mostly interested in the license in Rochester, MN, McLeod mostly interested in the licenses in Waterloo, IA and Marshaltown, IA Rochester s lot-number was 378 U.S. West bid in the first rounds were $313,378 in Waterloo and $62,378 in Marshaltown. McLeod got the point and stopped competing in Rochester Repeated Games Repeated Games and Rules The static constituent game might be repeated a finite and pre-specified number of times, or repeated indefinitely. In a repeated game, managers need to know the players, the rules, the information that each firm has, and the payoffs or profits. A manager must also distinguish between an action and a strategy. Strategies & Actions in Repeated Games An action is a single move that a player makes at a specified time, such as choosing an output level or a price. A strategy is a battle plan that specifies the full set of actions that a player will make throughout the game. It may involve actions that are conditional on prior actions of other players or on new information available at a given time. 25

26 Cooperation in a Repeated Prisoner s Dilemma Game Remember the American-United game of Chapter 12. The Nash equilibrium solution, if played only once, is both firms producing high (64 passengers) and making only $4.1 (Prisoner s Dilemma game). Assume the same game is repeated indefinitely. Now, firms must consider current and future profits, and must distinguish an action from a strategy. Strategies to Avoid a Prisoner s Dilemma Outcome Firms can follow a trigger strategy, in which a rival s defection from a collusive outcome triggers a punishment. If United uses this strategy, its action in the current period depends on American s observed actions in previous periods. Similarly for American. A Trigger Strategy for Airline Repeated Game American cheap-talks United that it will produce the 48 collusive or cooperative quantity in the 1 st period, but then its action will depend: if United produces 48 in period t, American will produce 48 in t + 1; if United produces 64 in period t, American will produce 64 in t + 1 and all subsequent periods. Nash-Equilibrium with no Prisoner s Dilemma United s best response strategy is to produce 48 in each period: the incremental profit from producing 64 one time does not compensate all future losses. If both firms follow the trigger strategy, the Nash-Equilibrium is the best outcome. In reality, cooperation may fail because of regulation, bounded rationality, or if a firm cares little about future profits. 26

27 Implicit Versus Explicit Collusion In most modern economies, explicit collusion among firms in an industry is illegal. However, antitrust laws do not strictly prohibit choosing the cooperative (cartel) quantity or price as long as no explicit agreement is reached. Implicit Collusion Firms may be able to engage in such implicit collusion or tacit collusion using trigger, tit-for-tat, or other similar strategies, as long as firms do not explicitly communicate each other. Tacit collusion lowers society s total surplus just as explicit collusion does. Finitely Repeated Games Assume American and United know that their game will be repeated only a finite number of times, T. They cheap-talk the trigger strategy mentioned before. Both firms know there is no punishment in the final period T. So it is basically a static Prisoner s Dilemma and both firms have a dominant strategy: produce 64. Going Backwards from the Last to the 1 st Period Period T: Each firm cheats and produces 64 for certain. Period T - 1: Nothing that each firm does will avoid the punishment in period T. So, it is better to cheat, produce 64 and earn extra profit. Period T - 2: Each firm cheats because they know both will cheat in T 1 anyway. Period T - 3 up to the 1 st period: Same logic No Cooperation Again! The only Nash equilibrium is 64 & 64 to occur in every period. Thus, maintaining an agreement to cooperate in any prisoners dilemma game is more difficult if there is a known end point and players have complete foresight. 27

28 Sequential Games Stages & Extensive Form Sequential game: many stages or decision points and players alternate moves (better, moves at different points in time) Extensive form: a branched diagram that shows the players, the sequence of moves, the actions players can take at each move, the information that each player has about previous moves, and the payoff function over all possible strategy combinations Subgame Perfect Nash-Equilibrium At any given stage, players play a subgame (actions and corresponding payoffs). Subgame perfect Nash equilibrium: if the players strategies form a Nash equilibrium in every subgame (including the overall game) Sequential Games Backward Induction for Subgame Perfect Nash-Equilibrium First determine the best response by the last player to move, then determine the best response for the player who made the next-to-last move, and so on until we reach the first move of the game. (Better, first determine the equilibrium in the last subgame, then determine the equilibrium in the next-to-last game, and so on until we reach the first subgame. 28

29 Stackelberg Oligopoly Game Two-stage, sequential-move oligopoly game: American, the leader firm, chooses its output level first. Given American s choice, United, the follower, picks an output level. All information is shown in extensive form. Stackelberg Oligopoly Game Backward Induction and Subgames A determines what U, the follower, will do in the 2 nd stage at the tree subgames: q U with highest profit at each node. A determines its best action in the 1 st stage given the choices of U in the 2 nd stage: q A with the highest profit. Subgame Perfect Nash-Equilibrium A chooses q A = 96 in the 1 st stage and U chooses q U = 48 in the 2 nd stage. In this equilibrium, neither firm wants to change its strategy. 29

30 Credible Threats The Nash equilibrium of the American-United static simultaneous game (Cournot with 3 options) was q A = q U = 96 and both firms earned $4.1 million (Chapter 12). The Subgame Perfect Nash Equilibrium of the American-United sequential game (Stackelberg) is q A = 96, q U = 48. American earns $4.6 million, but United only $2.3 million. Why different solutions? Credible Threat and First Mover Advantage For a firm s announced strategy to be a credible threat, rivals must believe that the firm s strategy is rational (works in the firm s best interest). In the simultaneous-move game, United will not believe a threat by American that it will produce 96. However, in the sequential game because American makes the 1 st move, its commitment to produce 96 is credible. Deterring Entry: Exclusion Contracts A mall has a single shoe store, the incumbent firm. The incumbent may pay the mall s owner b to add a clause to its rental agreement that guarantees exclusivity. If b is paid, the landlord agrees to rent the remaining space only to a no-shoe firm. two stages of the game. 1 st stage: incumbent decides whether to pay b to prevent entry. 2 nd stage, the potential rival decides whether to enter. If it enters, it incurs a fixed fee of F to build its store in the mall. 30

31 Deterring Entry: Exclusion Contracts Backward Induction for Subgame Perfect Nash-Equilibrium Last decision made by potential rival in 2 nd stage: the rival only plays one subgame. It enters if F 4 because π r = 4 F. Otherwise, stays out with π r = 0. Decision made by incumbent in 1 st stage knowing what potential rival will do in 2 nd stage: the decision to pay depends on the values of the exclusivity fee b and fixed cost F. Deterring Entry: Exclusion Contracts Three Possible Outcomes that Depend on b and F Blockaded entry (F > 4): Potential rival will stay out ensuring π r = 0. So, the incumbent avoids paying b and still earns the monopoly profit, π i = 10. Deterred entry (F 4, b 6): Potential rival will enter unless the incumbent pays the exclusivity fee. The incumbent chooses to pay b because b 6 ensures a profit at least as large as the duopoly profit of 4 (π i = 10 b 4). Accommodated entry (F 4, b > 6): Potential rival will enter to earn a positive profit of π r = 4 F. The incumbent does not pay the exclusivity fee because b is so high that it is better to ensure π i = 4 than earn less (π i = 10 b < 4). When to Pay the Exclusivity Fee? In short, the incumbent does not pay for an exclusive contract if the potential rival s cost of entry is prohibitively high (F > 4) or if the cost of the exclusive contract is too high (b > 6). 31

32 Entry Deterrence in a Repeated Game A grocery chain with a monopoly in many small towns faces potential entry by other firms in some or all of these towns. Figure shows the game in only one town. In the 1 st stage, the rival decides to enter the town or not. In the 2 nd stage, the incumbent decides between fighting with the rival (price war) or accommodating the rival. Entry Deterrence in a Repeated Game Accommodation if Game Played only Once If this game is played only once and if the profits are common knowledge, then the only subgame perfect Nash equilibrium is for entry to occur and for the incumbent to accommodate entry. 32

33 Entry Deterrence in a Repeated Game Price War if Repeated and Incomplete Information If the chain s profits are not common knowledge and the game will be played in many towns, the incumbent may want to fight back to build reputation or, better to give a (misleading) message on its own cost. Fighting the first rival is part of a rational long-run strategy and can be part of a subgame perfect Nash equilibrium in which entry is successfully deterred. Cost Strategies A firm may be able to gain a cost advantage over a rival by behaving strategically. We start by examining two cases. Moving First Lowers Own Marginal Cost A firm moves first to gain a marginal cost advantage over its rivals. It can lower its own marginal cost by using a capital investment or increasing the rate of learning by doing. Moving First Raises Rival s Marginal Cost A firm moves first to increase the rivals marginal cost by more than its own. 33

34 Investing to Lower Marginal Cost A monopoly considers installing robots on its assembly line that would lower its MC. Under normal conditions, this investment does not pay (investment cost > extra profit). But, a rival threatens to enter the market. In the game tree, the incumbent decides whether to invest in the first stage and the potential rival decides whether to enter in the second stage. Investing to Lower Marginal Cost Backward Induction First, rival decides entry decision in 2 nd stage: rival plays two subgames and decides the best action for each subgame based on highest profit values π r. Second, incumbent decides investment decision in 1 st stage after rival decided in 2 nd stage: incumbent plays one subgame and decides to invest (π i = 8 > π i = 4). 34

35 Investing to Lower Marginal Cost Subgame Perfect Nash Equilibrium The incumbent makes the unprofitable investment to deter the entry of potential rivals and earns π i = 8. Learning by Doing Learning by Doing: the more cumulative output a firm has produced, the lower its marginal cost, as its workers and managers learn by doing. In the presence of learning by doing, the first firm in a market may want to produce more than the quantity that maximizes its short-run profit, so that its marginal cost is lower than that of a late-entering rival. Two Real Examples: Aircraft and Computer Chips An aircraft manufacturer may price below current marginal cost in the short run, because of its steep learning curve. The price of the Lockheed L-1011 was below the static MC for its entire 14-year production run (Benkard, 2004). AMD s cost of computer chips was about 12% higher than Intel s cost. AMD had less learning by doing because it had produced fewer units (Salgado,2008). 35

36 Raising Rival s Costs A firm may benefit from using a strategy that raises its own cost but raises its rivals costs by more. Such strategies usually favor the first mover or incumbent against the rivals. Strategies for Incumbents to Raise Rival s Costs Lobby the government for more industry regulations that raise costs, as long as the legislation grandfathers existing firms plants (exemption). Increase the cost of switching by imposing a switching fee to customers that take their business elsewhere or designing products that don t work with the rival s. Use patents to prevent rivals entering the market and increasing competition. First-mover Advantage/Disadvantage: In all examples provided so far moving first was and advantage This is not always the case There are situations in which how moves first has a disadvantage One example: hold-up 36

37 Hold-up The holdup problem arises when two firms want to contract or trade with each other but one firm must move first by making a specific investment (can only be used in its transaction with the 2 nd firm). Problem: the 2 nd firm takes advantage of the 1 st firm. Consequences: If the 1 st firm does not anticipate the opportunistic behavior of the 2 nd firm and invests, it may earn no profit. If the 1 st firm anticipates it, then they will not invest and both firms lose. Hold-up In the Figure, ExxonMobil moves 1 st. It must decide to invest billions to obtain rights to drill for and refine oil in either Venezuela or another country. The Venezuelan government moves 2 nd and decides to nationalize or not. Problem: After ExxonMobil invests, it becomes a hostage of Venezuela because the investment cannot be transferred to other country. Outcome: Using backward induction, the Venezuelan government will nationalize in the 2 nd stage (profit π V of 32 > 20). Given this, ExxonMobil should invest in another country in the 1 st stage (profit π X of 10 > 8). 37

38 Minimizing hold-up Managers should seek ways to avoid losing money due to holdups. We illustrate five approaches with GM (car maker) and Fisher Body (parts manufacturer) below. The Five Strategies and Examples Contracts: The 2 nd -mover firm guarantees the 1 st -mover firm that it will not be exploited, GM gave a 10 year exclusive cost-plus contract to Fisher Body. Vertical Integration: After years of holdup problems, GM bought Fisher Body. Quasi-Vertical Integration: GM paid for and owned the specific capital assets. Reputation Building: GM can show its record of not acting opportunistically. Multiple or Open Sourcing: Firms using open-source software are not subject to a holdup problem. Moving too quickly The advantage of being the 1 st mover is consumer loyalty: later entrants find it difficult to take market share from the leader firm. However, moving too quickly has disadvantages too: the cost of entering quickly is higher, the odds of miscalculating demand are greater, and later rivals may build on the pioneer s research to produce a superior product. Moving Too Quickly Example Tagamet, 1 st entrant of a new class of anti-ulcer drugs, was extremely successful when it was introduced. Zantac, the 2 nd entrant, rapidly took the lion s share of the market. Tagamet moved too quickly: Zantac works similarly to Tagamet but has fewer side effects, can be taken less frequently, and was promoted more effectively. 38

39 Managerial Solution Managerial Problem Why have Intel s managers chosen to advertise aggressively while AMD engages in relatively little advertising? Solution A plausible game to explain the problem is in Figure 13.4: Intel decides on how much to invest in its advertising campaign before AMD can act. AMD then decides whether to advertise heavily. Managerial Solution Backward induction for the subgame perfect Nash equilibrium: Given how it expects AMD to behave, Intel intensively advertises because doing so produces a higher profit (π I = 8) than does the lower level of advertising (π I = 4). Thus, because Intel acts first and can commit to advertising aggressively, it can place AMD in a position where it makes more with a low-key advertising campaign. 39