【文章內(nèi)容簡介】 equilibrium ? Would a firm set price based on random choice assumption? 45 Chapter 1 The Battle of the Sexes Jim Wrestling Opera Wrestling Opera Joan 2,1 0,0 1,2 0,0 46 Chapter 1 The Battle of the Sexes Jim Wrestling Opera Wrestling Opera Joan 2,1 0,0 1,2 0,0 ? Pure Strategy ? Both watch wrestling ? Both watch opera ? Mixed Strategy ? Jim chooses wrestling ? Joan chooses wrestling 47 Chapter 1 Example A 1 2 1 2 B 30,40 70,50 80,80 20,100 ? What is the Nash equilibrium of the right table? If there is no Nash equilibrium involving pure strategies, check that players are indifferent among the actions used in their mixed strategies in equilibrium. Calculate the expected payoffs. 48 Chapter 1 博弈模型與競爭策略 警衛(wèi)與竊賊的博弈 警衛(wèi)睡覺 ,小偷去偷 ,小偷得益 B,警衛(wèi)被處分 D。 警衛(wèi)不睡，小偷去偷，小偷被抓受懲處 P, 警衛(wèi)不失不得。 警衛(wèi)睡覺，小偷不偷，小偷不失不得，警衛(wèi)得到休閑 R. 警衛(wèi)不睡，小偷不偷，都不得不失。 警衛(wèi) 睡覺 不睡覺 偷 不偷 竊賊 B, D P, 0 0, R 0, 0 49 Chapter 1 博弈模型與競爭策略 混合博弈的兩個原則 一 不能讓對方知道或猜到自己的選擇，因此必須在決策時采取隨機(jī)決策； 二 選擇每種策略的概率要恰好使對方無機(jī)可乘，對方無法通過有針對性的傾向于某種策略而得益 50 Chapter 1 博弈模型與競爭策略 警衛(wèi)是不是睡覺決定于小偷偷不偷的概率，而小偷偷不偷的概率在于小偷猜警衛(wèi)睡不睡覺 小偷一定來偷，警衛(wèi)一定不睡覺； 小偷一定不來偷，警衛(wèi)一定睡覺。 警衛(wèi)的得益 與小偷偷不偷的概率有關(guān) 51 Chapter 1 博弈模型與競爭策略 ? 若小偷來偷的概率為 偷 警衛(wèi)的得益為： R ( 1 偷 ) + (D) 偷 小偷認(rèn)為警衛(wèi)不會愿意得益為負(fù)，最多為零。 即 R/D= 偷 / ( 1 偷 ) 小偷偷不偷的概率等于 R與 D的比率 0 1 小偷偷 的概率 警衛(wèi)睡覺的期望得益 R D P偷 ?????52 Chapter 1 博弈模型與競爭策略 同樣的道理警衛(wèi)偷懶的概率 （睡覺） 睡 決定了小偷的得益為： (P) ( 1 睡 ) + (B) 睡 警衛(wèi)也認(rèn)為小偷不會愿意得益為負(fù)，最多為零。 即 B / P = ( 1 睡 )/ 睡 警衛(wèi)偷不偷懶的概率取決于 B與 P的比率 有趣的激勵悖論 管理經(jīng)濟(jì)學(xué)考什么？ 0 1 警衛(wèi)偷懶 的概率 小偷的期望得益 P睡 P B ???53 Chapter 1 Repeated Games ? Oligopolistic firms play a repeated game. ? With each repetition of the Prisoners’ Dilemma, firms can develop reputations about their behavior and study the behavior of their petitors. 54 Chapter 1 Pricing Problem Firm 1 Low Price High Price Low Price High Price Firm 2 10, 10 100, 50 50, 50 50, 100 55 Chapter 1 Pricing Problem Firm 1 Low Price High Price Low Price High Price Firm 2 10, 10 100, 50 50, 50 50, 100 ? Nonrepeated game ? Strategy is Low1, Low2 ? Repeated game ? Titfortat strategy is the most profitable 56 Chapter 1 Repeated Games ? Conclusion: ? With repeated game ?The Prisoners’ Dilemma can have a cooperative oute with titfortat strategy 57 Chapter 1 Repeated Games ? Conclusion: ? This is most likely to occur in a market with: ?Few firms ?Stable demand ?Stable cost 58 Chapter 1 Repeated Games ? Conclusion ? Cooperation is difficult at best since these factors may change in the longrun. 59 Chapter 1 Oligopolistic Cooperation in the Water Meter Industry ? Characteristics of the Market ? Four Producers ?Rockwell International (35%), Badger Meter, Neptune Water Meter Company, and Hersey Products (Badger, Neptune, and Hersey bined have about a 50 to 55% share) 60 Chapter 1 Oligopolistic Cooperation in the Water Meter Industry ? Characteristics of the Market ? Very inelastic demand ?Not a significant part of the budget 61 Chapter 1 ? Characteristics of the Market ? Stable demand ? Long standing relationship between consumer and producer ?Barrier ? Economies of scale ?Barrier Oligopolistic Cooperation in the Water Meter Industry 62 Chapter 1 ? Characteristics of the Market ?This is a Prisoners’ Dilemma ?Lower price to a petitive level ?Cooperate ? Repeated Game ? Question ? Why has cooperation prevailed? Oligopolistic Cooperation in the Water Meter Industry 63 Chapter 1 ? What Do You Think? ? Is there cooperation collusion in the airline industry? Competition and Collusion in the Airline Industry 64 Chapter 1 Example ABC Advertise Don’t Advertise Advertise Don’t advertise NBC 100, 100 300, 0 200, 200 0,300 ? Right table shows a Prisoner’s Dilemma game in which the players are the two works ABC and NBC. Their strategies are advertise or not advertise their new fall lineup. If they don’t advertise, they will split the market and they will have saved on advertising expenditure. If they both advertising, ratings are high, but so are costs, so profits fall. If one advertises and the other doesn’t, there is a clear gain to be made. Profits are indicated in the payoff matrix in millions of dollars per year. 65 Chapter 1 Example (Cont.) ? What is the Nash equilibrium if this game is played only once? ? Now consider a repeated game based on above table. Suppose ABC refuses to advertise in the first period and continues not to advertise as long as NBC doesn’t advertise. But if NBC fails even once to cooperate, ABC will revert forever to the safe policy of advertising. Although this is supposed to be an infinitely repeated game, consider just a tenperiod game make the algebra easier. Calculate the sum of NBC’s profits over time if it adopts a parallel strategy. Then calculate the sum of NBC’s profits over time if it takes advantage of ABC’s willingness to corporate by choosing to advertise in the first period. Comparing these two ine streams, what will NBC do? 66 Chapter 1 Sequential Games ? Players move in turn ? Players must think through the possible actions and rational reactions of each player 67 Chapter 1 Sequential Games ? Examples ?Responding to a petitor’s ad campaign ? Entry decisions ? Responding to regulatory policy 68 Chapter 1 ? Scenario ? Two new (sweet, crispy) cereals ? Successful only if each firm produces one cereal ? Sweet will sell better ? Both still profitable with only one producer Sequential Games The Extensive Form of