CHAPTER 13 GAMETHEORYAND COMPETITIVESTRATEGY QUESTIONS FOR REVIEW 1.What is the difference between a cooperative and a noncooperative game? Give an example ofeach. In a noncooperative game the players do not formally communicate in an effort to coordinate their actions.They are aware of one another's existence,but act independently The primary noncooperative game is that a binding contract,ie.,an agreement between the parties to which both parties must adhere,is possible in the former,but not in the latter.An example ofa cooperative game would be a formal cartel agreement,such as OPEC.or a joint venture.An example of a noncooperative game would be a race in research and development to obtain a patent. 2.What is a dominant strategy?Why is an equilibrium stable in dominant strategies? A dominant strategy is one that is best no matter what action is taken by the other party to the game.When both players have dominant strategies the outcome is stable because neither party has an incentive to change. 3.Explain the meaning of a Nash equilibrium.How does it differ from an equilibrium in dominant strategies? A Nash equilibrium isan outcome where both play believe that they are doingthe can,given the action of th game is in equilibriun if neither player has an incentive to change his or her choice,unless there is a change by the other player.The key feature that distinguishes a Nash equilibrium from an equilibrium in dominant strategies is the dependence on the opponent's behavior.An equilibrium in dominant strategies results if each player has a best choice regardless of the other player's choice.Every dominant strategy but the revere does not hold. 4.How does a Nash equilibrium differ from a game's maximin solution?In what situations is a maximin solution a more likely outcome than a Nash equilibrium? A maximin strategy is one in which each player determines the worst outcome for each of the opponent's actions and chooses the option that maximizes the minimum n that be arnd.Unlke the Nash them not require players to react to an opporent's choice. If no dominant strategy exi (in which case outcomes depend on the opponent's behavior),players can reduce the uncertainty inherent in relying on the opponent's rationality by conservatively following a maximin strategy.The maximin solution is more likely than the Nash
CHAPTER 13 GAME THEORY AND COMPETITIVE STRATEGY 一、QUESTIONS FOR REVIEW 1. What is the difference between a cooperative and a noncooperative game? Give an example of each. In a noncooperative game the players do not formally communicate in an effort to coordinate their actions. They are aware of one another’s existence, but act independently. The primary difference between a cooperative and a noncooperative game is that a binding contract, i.e., an agreement between the parties to which both parties must adhere, is possible in the former, but not in the latter. An example of a cooperative game would be a formal cartel agreement, such as OPEC, or a joint venture. An example of a noncooperative game would be a race in research and development to obtain a patent. 2. What is a dominant strategy? Why is an equilibrium stable in dominant strategies? A dominant strategy is one that is best no matter what action is taken by the other party to the game. When both players have dominant strategies, the outcome is stable because neither party has an incentive to change. 3. Explain the meaning of a Nash equilibrium. How does it differ from an equilibrium in dominant strategies? A Nash equilibrium is an outcome where both players correctly believe that they are doing the best they can, given the action of the other player. A game is in equilibrium if neither player has an incentive to change his or her choice, unless there is a change by the other player. The key feature that distinguishes a Nash equilibrium from an equilibrium in dominant strategies is the dependence on the opponent’s behavior. An equilibrium in dominant strategies results if each player has a best choice, regardless of the other player’s choice. Every dominant strategy equilibrium is a Nash equilibrium but the reverse does not hold. 4. How does a Nash equilibrium differ from a game’s maximin solution? In what situations is a maximin solution a more likely outcome than a Nash equilibrium? A maximin strategy is one in which each player determines the worst outcome for each of the opponent’s actions and chooses the option that maximizes the minimum gain that can be earned. Unlike the Nash equilibrium, the maximin solution does not require players to react to an opponent’s choice. If no dominant strategy exists (in which case outcomes depend on the opponent’s behavior), players can reduce the uncertainty inherent in relying on the opponent’s rationality by conservatively following a maximin strategy. The maximin solution is more likely than the Nash
solution in cases where there is a higher probability of irrational (non-optimizing) behavior. 5.What is a"tit-for-tat"strategy?Why is it a rational strategy for the infinitely repeated prisoners'dilemma? A player ollowing a "tit-for-tat"strategy will cooperate as bng as his or be opponent is cooperating and will switch to a noncooperative strategy if their opponent switches strategies.When the competitors assume that they will be repeating their interaction in every future period.the long-term gains from erating will outweigh anysort-tem gains from not operating Because the -tat strategy encourages cooperation in infinitely repeated games,it is rational 6.Consider a game in which the prisoners'dilemma is repeated 10 times and both players are rational and fully informed.Is a tit-for-tat strategy optimal in this case?Under what conditions would such a strategy be optimal? Since cooperation will unravel from the last period back to the first period,the "tit-for-tatstrategy is notoptimal when there is a finite number of periods and both players anticip ate the competitor's in every period G iven tha at there is response possible in the eleventh period for action in the tenth (and last)period cooperation breaks down in the last period.Then,knowing that there is no cooperation in the last period,players should maximize their self-interest by not However,if there is some doubt about whether the opponent has fully anticipated the consequences of the "tit-for-tat"strategy in the final period,the game will not unravel and the"tit-for-tat"strategy can be optimal. 7.Suppose you and your competitor are playing the pricing game shown in Table 13.8.Both of you must announce your prices at the same time.Can you rove by promising you competitor that you If the game is to be played only aw times,there is little to gain.If you are Firm and promise to announce a high price.Firm 2 will undercut you and you will end up with a payoff of-50.However,next period you will undercut too,and both fims will earn 10.If the game is played many times,there is a better chance that Fim 2 will realize that if it high p e.the long-term payoff of 50 each period is better than 10at first and 10 thereaft 8.What is meant by "first-mover advantage"?Give an example of a gaming situation with a first-mover advantage. A "first-mover"advantage can occur in a game where the first player to act receives the highest payoff.The first-mover signals his or her choice to the opponent,and the opponent must choose a response.given this signal.The first-mover goes on the offensive and the second-mover respo onds defensively.In many recreational
solution in cases where there is a higher probability of irrational (non-optimizing) behavior. 5. What is a “tit-for-tat” strategy? Why is it a rational strategy for the infinitely repeated prisoners’ dilemma? A player following a “tit-for-tat” strategy will cooperate as long as his or her opponent is cooperating and will switch to a noncooperative strategy if their opponent switches strategies. When the competitors assume that they will be repeating their interaction in every future period, the long-term gains from cooperating will outweigh any short-term gains from not cooperating. Because the “tit-for-tat” strategy encourages cooperation in infinitely repeated games, it is rational. 6. Consider a game in which the prisoners’ dilemma is repeated 10 times and both players are rational and fully informed. Is a tit -for-tat strategy optimal in this case? Under what conditions would such a strategy be optimal? Since cooperation will unravel from the last period back to the first period, the “tit-for-tat” strategy is not optimal when there is a finite number of periods and both players anticipate the competitor’s response in every period. Given that there is no response possible in the eleventh period for action in the tenth (and last) period, cooperation breaks down in the last period. Then, knowing that there is no cooperation in the last period, players should maximize their self-interest by not cooperating in the second-to-last period. This unraveling occurs because both players assume that the other player has considered all consequences in all periods. However, if there is some doubt about whether the opponent has fully anticipated the consequences of the “tit-for-tat” strategy in the final period, the game will not unravel and the “tit-for-tat” strategy can be optimal. 7. Suppose you and your competitor are playing the pricing game shown in Table 13.8. Both of you must announce your prices at the same time. Can you improve your outcome by promising your competitor that you will announce a high price? If the game is to be played only a few times, there is little to gain. If you are Firm 1 and promise to announce a high price, Firm 2 will undercut you and you will end up with a payoff of -50. However, next period you will undercut too, and both firms will earn 10. If the game is played many times, there is a better chance that Firm 2 will realize that if it matches your high price, the long-term payoff of 50 each period is better than 100 at first and 10 thereafter. 8. What is meant by “first-mover advantage”? Give an example of a gaming situation with a first-mover advantage. A “first-mover” advantage can occur in a game where the first player to act receives the highest payoff. The first-mover signals his or her choice to the opponent, and the opponent must choose a response, given this signal. The first-mover goes on the offensive and the second-mover responds defensively. In many recreational
games.from chess to football the first-mover has an advantage.In many markets the firstfirm to product canet the standard In some cases,the standard-setting power of the first mover becomes so pervasive in the market that the brand name of the product becomes synonymous with the product,e.g,"Kleenex"the name of Kleenex-brand facial tissue.is used by many consumers to refer to facial tissue ofany brand. 9.What is a "strategic move"?How can the development of a certain kind of reputation be a strategic move? A strategic move involves a commitment to reduce one's options The strateg move might not seem rational outside the context of the game in which it is played but it is rational given the anticipated response of the other player.Random responses to an opponent's action may not appear to be rational,but developing a reputation of being unpredictable oould lead to higher payoffs in the long run. Another exampl would be making a promise to give a unt to all p consumers if you give a discount toone.Such a move makes the firm vulnerabk but the goal of such a strategic move is to signal to rivals that you won't be discounting price and hope that your rivals follow suit. 10.Can the threat of a price war deter entry by potential competitors?What actions might a firm take to make this threat credible? Both the incumbent and the potential entrant know that a price war will leave their firms worse off Normally uch a threat is not crdibe.Thus the incumbent must make his or her threat ofa price war belevable by signalingto the potenti entrant that a price war will result if entry occurs.One strategic move is to increase capacity,signaling a lower future price,and another is to engage in apparently irrational behavior.Both types of strategic behavior might deter entry. but for different reasons.While an inc sein capacity reduces expected profits by reducing prices rrational behavio expected profits by increasin uncertainty,hence increasing the rate at which future profits must be discounted into the present. 11.A strategic move limits one's flexibility and yet gives one an advantage.Why? How might a strategic move give one an advantage in bargaining? A strategic move influences conditional behavior by the opponent.If the game is well understood and the reaction can be pre icted.a strategi e es the play transac a bargain, mphcit or explicit.In every bargain,we assume that both parties attempt to maximize their self-interest.Strategic moves by one plaver provide signals to which another player reacts.If a bargaining game is played only once (so no reputations are involved).the plavers might act strategically to maximize their payoffs.If bargaining is repeated,players might act strategically to establish reputations for expected negotiations 12.Why is the winner's curse potentially a problem for a bidder in a common value auction but not in a private value auction?
games, from chess to football, the first-mover has an advantage. In many markets, the first firm to introduce a product can set the standard for competitors to follow. In some cases, the standard-setting power of the first mover becomes so pervasive in the market that the brand name of the product becomes synonymous with the product, e.g., “Kleenex,” the name of Kleenex-brand facial tissue, is used by many consumers to refer to facial tissue of any brand. 9. What is a “strategic move”? How can the development of a certain kind of reputation be a strategic move? A strategic move involves a commitment to reduce one’s options. The strategic move might not seem rational outside the context of the game in which it is played, but it is rational given the anticipated response of the other player. Random responses to an opponent’s action may not appear to be rational, but developing a reputation of being unpredictable could lead to higher payoffs in the long run. Another example would be making a promise to give a discount to all previous consumers if you give a discount to one. Such a move makes the firm vulnerable, but the goal of such a strategic move is to signal to rivals that you won’t be discounting price and hope that your rivals follow suit. 10. Can the threat of a price war deter entry by potential competitors? What actions might a firm take to make this threat credible? Both the incumbent and the potential entrant know that a price war will leave their firms worse off. Normally, such a threat is not credible. Thus, the incumbent must make his or her threat of a price war believable by signaling to the potential entrant that a price war will result if entry occurs. One strategic move is to increase capacity, signaling a lower future price, and another is to engage in apparently irrational behavior. Both types of strategic behavior might deter entry, but for different reasons. While an increase in capacity reduces expected profits by reducing prices, irrational behavior reduces expected profits by increasing uncertainty, hence increasing the rate at which future profits must be discounted into the present. 11. A strategic move limits one’s flexibility and yet gives one an advantage. Why? How might a strategic move give one an advantage in bargaining? A strategic move influences conditional behavior by the opponent. If the game is well understood and the opponent’s reaction can be predicted, a strategic move leaves the player better off. Economic transactions involve a bargain, whether implicit or explicit. In every bargain, we assume that both parties attempt to maximize their self-interest. Strategic moves by one player provide signals to which another player reacts. If a bargaining game is played only once (so no reputations are involved), the players might act strategically to maximize their payoffs. If bargaining is repeated, players might act strategically to establish reputations for expected negotiations. 12. Why is the winner’s curse potentially a problem for a bidder in a common value auction but not in a private value auction?
The winner's curse states that"The winner of a common value auction is likely to be madeworseof(than notwinning)because the winner was overly optimistic and,as a consequen,bid more for the item than it was actually worth In a private value auction,you are aware of your own reservation price,and will bid accordingly Once the price has escalated above your reservation price.you will no bnger bid.If you win,it is because the winning bid was below your reservation price.In a common value auction,you do not know the exact value of the good you are bidding 0n. The winne end to be valu the good,assuming that some bidders overestimate and some underestimate.If al bids are below the actual value,then there is no winner's curse. 二、EXERCISES 1.In many oligopolistic industries,the same firms compete over a long period of time,setting prices and observing each other's behavior repeatedly.Given that the number of repetitions is large,why don't collusive outcomes typically result? If gamesar repeated indefinitely and all players know all payoffs rational behavior will lead to apparently coll ve outcomes,1.e. the same outcomes tha would result if firms were actively colluding.All payoffs.bowever.might not be known by all players.Sometimes the payoffs of other firms can only be known by engaging in extensive (and costly)information exchanges or by making a move and observing rivals'responses.Also.successful collusion encourages entry.Perhaps the greates poblem in maintaining is that change in marke conditions change the collusive price and quantity The firms then have to repeatedly change their agreement on price and quantity,which is costly.and this increases the ability of one firm to cheat without being discovered. 2.Many industries are often plagued by overcapacity-firms simultaneously make maior investments in capacity exp ansion,so total cap acity far exceeds demand.This hap t only in industries s in which de nd is highly volatile and unpredictable, but also in industries in whie h demand i fairly sta Wha factors lead to overcapacity?Explain each briefly. In Chapter 12.we found that excess capacity may arise in industries with easy entry and differentiated products.In the monopolistic competition model, downward-sloping demand curvesfor eachfirm lead to output with average cost above minim The between the res sulting outpu output at minimum long-run average cost is defined as excess capacity. n this chapter,we saw that overcapacity oould be used to deter new entry;that is, investments in capacity expansion could convince potential competitors that entry would be unprofitable.(Note that although threats of capacity expansion may deter entry.these threats must be credible. 3.Two computer firms,A and B.are planning to market network systems for office information management. Each can dev lop either a fast high-quality system (H),or a slower,low-quality system (L).Market research
The winner’s curse states that “The winner of a common value auction is likely to be made worse off (than not winning) because the winner was overly optimistic and, as a consequence, bid more for the item than it was actually worth.” In a private value auction, you are aware of your own reservation price, and will bid accordingly. Once the price has escalated above your reservation price, you will no longer bid. If you win, it is because the winning bid was below your reservation price. In a common value auction, you do not know the exact value of the good you are bidding on. The winner will tend to be the person who has most overestimated the value of the good, assuming that some bidders overestimate and some underestimate. If all bids are below the actual value, then there is no winner’s curse. 二、EXERCISES 1. In many oligopolistic industries, the same firms compete over a long period of time, setting prices and observing each other’s behavior repeatedly. Given that the number of repetitions is large, why don’t collusive outcomes typically result? If games are repeated indefinitely and all players know all payoffs, rational behavior will lead to apparently collusive outcomes, i.e., the same outcomes that would result if firms were actively colluding. All payoffs, however, might not be known by all players. Sometimes the payoffs of other firms can only be known by engaging in extensive (and costly) information exchanges or by making a move and observing rivals’ responses. Also, successful collusion encourages entry. Perhaps the greatest problem in maintaining a collusive outcome is that changes in market conditions change the collusive price and quantity. The firms then have to repeatedly change their agreement on price and quantity, which is costly, and this increases the ability of one firm to cheat without being discovered. 2. Many industries are often plagued by overcapacity-firms simultaneously make major investments in capacity expansion, so total capacity far exceeds demand. This happens not only in industries in which demand is highly volatile and unpredictable, but also in industries in which demand is fairly stable. What factors lead to overcapacity? Explain each briefly. In Chapter 12, we found that excess capacity may arise in industries with easy entry and differentiated products. In the monopolistic competition model, downward-sloping demand curves for each firm lead to output with average cost above minimum average cost. The difference between the resulting output and the output at minimum long-run average cost is defined as excess capacity. In this chapter, we saw that overcapacity could be used to deter new entry; that is, investments in capacity expansion could convince potential competitors that entry would be unprofitable. (Note that although threats of capacity expansion may deter entry, these threats must be credible.) 3. Two computer firms, A and B, are planning to market network systems for office information management. Each firm can develop either a fast, high-quality system (H), or a slower, low-quality system (L). Market research
indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix Firm B H H 50,40 60,45 FirmA L 55,55 15,20 a If both firms make their decisions at the same time and follow maximin (low-risk)strategies,what willthe outcome be? With a maximin strategy,a firm determines the worst outcome for each option,ther chooses the option that maximizes the payoff among the worst outcomes.If Firm A chooses H,the worst payoff would occur if Firm Bchooses H:A's payoff would be 50. If Firm A chooses L.the worst pavoff would occur if Firm B chooses L:A's pavoff would be 15.With a maximin strategy.A therefore chooses H.If Firm B cho payoff would occur ifFirm AchoosesL:the payoff would be 20.If Firr B chooses H the worst payoff,40.would oecur if Firm A chooses H.With a maximin strategy.B therefore chooses H.So under maximin,both A and B produce a high-quality system. Suppose both firms try to maximize profits,but Firm A has a head start in planning,and can commit first.Now what will the outcome be?What will the e outcome be if Firm B has a head start in planning and I can commit first? If Firm A can commit first,it will choose H because it knows that Firm B will rationally choose L.since L gives a higher payoff to B(45 vs.40).This gives Firm A a payoff of 60.If Firm A instead committed to L B would choose H (55 vs.20) giving A 55 instead of 60.If Firm B can commit first,it will choose H because it s that Firm A will rationally chooseL since L gives a higher payoff to A(55 vs 50 This gives Firm Ba payoffof 55 Getting a head start costs money (you have to gear up a large engineering team).Now consider the two-stage game in which first,each firm decides how much money to spend to speed up its planning.and second,it announces which product (H or L)it will produce.Which firm will spend mor speed planning?How will it nd?Should the other firm spend anything to speed up its planning?Explain In this game.there is an apparent advantage to being the first mover.If A move first,its profit is 60.If it moves second,its profit is 55,a difference of 5.Thus,it would be willing to spend up to 5 for the option of announcing first.On the other
indicates that the resulting profits to each firm for the alternative strategies are given by the following payoff matrix: Firm B H L H 50, 40 60, 45 Firm A L 55, 55 15, 20 a. If both firms make their decisions at the same time and follow maximin (low-risk) strategies, what will the outcome be? With a maximin strategy, a firm determines the worst outcome for each option, then chooses the option that maximizes the payoff among the worst outcomes. If Firm A chooses H, the worst payoff would occur if Firm B chooses H: A’s payoff would be 50. If Firm A chooses L, the worst payoff would occur if Firm B chooses L: A’s payoff would be 15. With a maximin strategy, A therefore chooses H. If Firm B chooses L, the worst payoff would occur if Firm A chooses L: the payoff would be 20. If Firm B chooses H, the worst payoff, 40, would occur if Firm A chooses H. With a maximin strategy, B therefore chooses H. So under maximin, both A and B produce a high-quality system. b. Suppose both firms try to maximize profits, but Firm A has a head start in planning, and can commit first. Now what will the outcome be? What will the outcome be if Firm B has a head start in planning and can commit first? If Firm A can commit first, it will choose H, because it knows that Firm B will rationally choose L, since L gives a higher payoff to B (45 vs. 40). This gives Firm A a payoff of 60. If Firm A instead committed to L, B would choose H (55 vs. 20), giving A 55 instead of 60. If Firm B can commit first, it will choose H, because it knows that Firm A will rationally choose L, since L gives a higher payoff to A (55 vs. 50). This gives Firm B a payoff of 55. c. Getting a head start costs money (you have to gear up a large engineering team). Now consider the two-stage game in which first, each firm decides how much money to spend to speed up its planning, and second, it announces which product (H or L) it will produce. Which firm will spend more to speed up its planning? How much will it spend? Should the other firm spend anything to speed up its planning? Explain. In this game, there is an apparent advantage to being the first mover. If A moves first, its profit is 60. If it moves second, its profit is 55, a difference of 5. Thus, it would be willing to spend up to 5 for the option of announcing first. On the other