微观经济学（平狄克、鲁宾费尔德）第六版课后答案-微观经济学 英文原版-CH13-PINDYCK

1、Chapter 13Game Theory and Competitive StrategyTopics to be DiscussedGaming and Strategic DecisionsDominant StrategiesThe Nash Equilibrium RevisitedRepeated Games2Topics to be DiscussedSequential GamesThreats, Commitments, and CredibilityEntry DeterrenceBargaining StrategyAuctions3Gaming and Strategi

2、c DecisionsGame is any situation in which players (the participants) make strategic decisionsEx: firms competing with each other by setting prices, group of consumers bidding against each other in an auctionStrategic decisions result in payoffs to the players: outcomes that generate rewards or benef

3、its4Gaming and Strategic DecisionsGame theory tries to determine optimal strategy for each playerStrategy is a rule or plan of action for playing the gameOptimal strategy for a player is one that maximizes the expected payoffWe consider players who are rational they think through their actions5Gamin

4、g and Strategic Decisions“If I believe that my competitors are rational and act to maximize their own profits, how should I take their behavior into account when making my own profit-maximizing decisions?”(Text, p. 474)6Noncooperative vs. Cooperative GamesCooperative GamePlayers negotiate binding co

5、ntracts that allow them to plan joint strategiesExample: Buyer and seller negotiating the price of a good or service or a joint venture by two firms (i.e., Microsoft and Apple) Binding contracts are possible7Noncooperative vs. Cooperative GamesNoncooperative GameNegotiation and enforcement of bindin

6、g contracts between players is not possibleExample: Two competing firms, assuming the others behavior, independently determine pricing and advertising strategy to gain market shareBinding contracts are not possible8Noncooperative vs. Cooperative Games“The strategy design is based on understanding yo

7、ur opponents point of view, and (assuming your opponent is rational) deducing how he or she is likely to respond to your actions.” (Text, p. 475)9Gaming and Strategic DecisionsAn Example: How to buy a dollar billAuction a dollar billHighest bidder receives the dollar in return for the amount bidSeco

8、nd highest bidder must pay the amount he or she bid but gets nothing in returnHow much would you bid for a dollar?Typically bid more for the dollar when faced with loss as second highest bidder10Acquiring a CompanyScenarioCompany A: The AcquirerCompany T: The TargetA will offer cash for all of Ts sh

9、aresThe value and viability of T depends on the outcome of a current oil exploration project11Acquiring a CompanyProject failure: Ts value = $0Project success: Ts value = $100/shareAll outcomes in between equally likelyTs value will be 50% greater with As management12Acquiring a CompanyScenarioA mus

10、t submit the proposal before the exploration outcome is knownT will not choose to accept or reject until after the outcome is known only to TCompany T will accept any offer that is greater than the per share value of the company under current managementHow much should A offer?13Dominant StrategiesDo

11、minant Strategy is one that is optimal no matter what an opponent doesAn ExampleA and B sell competing productsThey are deciding whether to undertake advertising campaigns14Payoff Matrix for Advertising GameFirm AAdvertiseDontAdvertiseAdvertiseDontAdvertiseFirm B10, 515, 010, 26, 815Payoff Matrix fo

12、r Advertising GameObservationsA: regardless of B, advertising is the bestB: regardless of A, advertising is bestFirm AAdvertiseDontAdvertiseAdvertiseDontAdvertiseFirm B10, 515, 010, 26, 816Payoff Matrix for Advertising GameObservationsDominant strategy for A and B is to advertiseDo not worry about t

13、he other playerEquilibrium in dominant strategyFirm AAdvertiseDontAdvertiseAdvertiseDontAdvertiseFirm B10, 515, 010, 26, 817Dominant StrategiesEquilibrium in dominant strategiesOutcome of a game in which each firm is doing the best it can regardless of what its competitors are doingOptimal strategy

14、is determined without worrying about the actions of other playersHowever, not every game has a dominant strategy for each player18Dominant StrategiesGame Without Dominant StrategyThe optimal decision of a player without a dominant strategy will depend on what the other player doesRevising the payoff

15、 matrix, we can see a situation where no dominant strategy exists1910, 515, 020, 26, 8Firm AAdvertiseDontAdvertiseAdvertiseDontAdvertiseFirm BModified Advertising Game2010, 515, 020, 26, 8Firm AAdvertiseDontAdvertiseAdvertiseDontAdvertiseFirm BModified Advertising GameObservationsA: No dominant stra

16、tegy; depends on Bs actionsB: Dominant strategy is to advertiseFirm A determines Bs dominant strategy and makes its decision accordingly21The Nash Equilibrium RevisitedA dominant strategy is stable, but in many games one or more party does not have a dominant strategyA more general equilibrium conce

17、pt is the Nash Equilibrium introduced in Chapter 12A set of strategies (or actions) such that each player is doing the best it can given the actions of its opponents22The Nash Equilibrium RevisitedNone of the players have incentive to deviate from its Nash strategy, therefore it is stableIn the Cour

18、not model, each firm sets its own price assuming the other firms outputs are fixed. Cournot equilibrium is a Nash Equilibrium.23The Nash Equilibrium RevisitedDominant Strategy“Im doing the best I can no matter what you do. Youre doing the best you can no matter what I do.”Nash Equilibrium“Im doing t

19、he best I can given what you are doing. Youre doing the best you can given what I am doing.”Dominant strategy is a special case of Nash equilibrium24The Nash Equilibrium RevisitedTwo cereal companies face a market in which two new types of cereal can be successfully introduced, provided each type is

20、 introduced by only one firmProduct Choice ProblemMarket for one producer of crispy cerealMarket for one producer of sweet cerealEach firm only has the resources to introduce one cerealNoncooperative25Product Choice ProblemFirm 1CrispySweetCrispySweetFirm 2-5, -510, 10-5, -510, 1026Product Choice Pr

21、oblemFirm 1CrispySweetCrispySweetFirm 2-5, -510, 10-5, -510, 10If Firm 1 hears Firm 2 is introducing a new sweet cereal, its best action is to make crispyBottom left corner is Nash equilibriumWhat is other Nash Equilibrium?27Beach Location GameScenarioTwo competitors, Y and C, selling soft drinksBea

22、ch is 200 yards longSunbathers are spread evenly along the beachPrice Y = Price CCustomer will buy from the closest vendor28Beach Location GameWhere will the competitors locate (i.e., where is the Nash equilibrium)?Will want to all locate in center of beachSimilar to groups of gas stations, car deal

23、erships, etc.Ocean0BBeachA200 yardsC29The Nash Equilibrium RevisitedMaximin Strategies - ScenarioTwo firms compete selling file encryption softwareThey both use the same encryption standard (files encrypted by one software can be read by the other - advantage to consumers)Firm 1 has a much larger ma

24、rket share than Firm 2Both are considering investing in a new encryption standard30Maximin StrategyFirm 1Dont investInvestFirm 20, 0-10, 1020, 10-100, 0Dont investInvest31Maximin StrategyFirm 1Dont investInvestFirm 20, 0-10, 1020, 10-100, 0Dont investInvestObservationsDominant strategy Firm 2: Inves

25、tFirm 1 should expect Firm 2 to investNash equilibriumFirm 1: investFirm 2: InvestThis assumes Firm 2 understands the game and is rational32Maximin StrategyFirm 1Dont investInvestFirm 20, 0-10, 1020, 10-100, 0Dont investInvestObservationsIf Firm 2 does not invest, Firm 1 incurs significant lossesFir

26、m 1 might play dont investMinimize losses to 10 maximin strategy33Maximin StrategyIf both are rational and informedBoth firms investNash equilibriumIf Player 2 is not rational or completely informedFirm 1s maximin strategy is to not investFirm 2s maximin strategy is to investIf 1 knows 2 is using a

27、maximin strategy, 1 would invest34Maximin StrategyIf Firm 1 is unsure about what Firm 2 will do, it can assign probabilities to each possible actionCould use a strategy that maximizes its expected payoffFirm 1s strategy depends critically on its assessment of probabilities for Firm 235Prisoners Dile

28、mmaPrisoner AConfessDont ConfessConfessDontConfessPrisoner B-5, -5-1, -10-2, -2-10, -136Prisoners DilemmaPrisoner AConfessDont ConfessConfessDontConfessPrisoner B-5, -5-1, -10-2, -2-10, -1What is the:Dominant strategyNash equilibriumMaximin solutionDominant strategies are also maximin strategiesBoth

29、 confess is both Nash equilibrium and maximin solution37Mixed StrategyPure StrategyPlayer makes a specific choice or takes a specific actionMixed StrategyPlayer makes a random choice among two or more possible actions, based on a set of chosen probabilities38Matching PenniesPlayer AHeadsTailsHeadsTa

30、ilsPlayer B1, -1-1, 11, -1-1, 139Matching PenniesPure strategy: No Nash equilibriumNo combination of head and tails leaves both players better offMixed strategy: Random choice is a Nash equilibriumPlayer AHeadsTailsHeadsTailsPlayer B1, -1-1, 11, -1-1, 140Matching PenniesPlayer A might flip coin play

31、ing heads with probability and tails with probabilityIf both players follow this strategy, there is a Nash equilibrium both players will be doing the best they can given what their opponent is doingAlthough the outcome is random, the expected payoff is 0 for each player41Mixed StrategyOne reason to

32、consider mixed strategies is when there is a game that does not have any Nash equilibriums in pure strategyWhen allowing for mixed strategies, every game has a Nash equilibriumMixed strategies are popular for games like pokerA firm might not find it reasonable42The Battle of the SexesJimWrestlingOpe

33、raWrestlingOperaJoan2,10,01,20,043The Battle of the SexesPure StrategyBoth watch wrestlingBoth watch operaMixed StrategyJim chooses wrestlingJoan chooses wrestlingJim WrestlingOperaWrestlingOperaJoan2,10,01,20,044Repeated GamesGame in which actions are taken and payoffs are received over and over ag

34、ainOligopolistic firms play a repeated gameWith each repetition of the Prisoners Dilemma, firms can develop reputations about their behavior and study the behavior of their competitors45Pricing ProblemFirm 1Low PriceHigh PriceLow PriceHigh PriceFirm 210, 10100, -5050, 50-50, 10046Pricing ProblemHow

35、does a firm find a strategy that would work best on average against all or almost all other strategies?Tit-for-tat strategyRepeated game strategy in which a player responds in kind to an opponents previous play, cooperating with cooperative opponents and retaliating against uncooperative ones47Tit-f

36、or-Tat StrategyWhat if the game is infinitely repeated?Competitors repeatedly set price every month, foreverTit-for-tat strategy is rationalIf competitor charges low price and undercuts firmWill get high profits that month but know I will lower price next monthBoth of us will get lower profits if ke

37、ep undercutting, so not rational to undercut48Tit-for-Tat StrategyWhat if repeated a finite number of times?If both firms are rational, they will charge high prices until the last monthAfter the last month, there is no retaliation possibleBut in the month before last month, knowing that will charge

38、low price in last month, will charge low price in month beforeKeep going and see that only rational outcome is for both firms to charge low price every month49Tit-for-Tat StrategyIf firms dont believe their competitors are rational or think perhaps they arent, cooperative behavior is a good strategy

39、Most managers dont know how long they will be competing with their rivalsIn a repeated game, prisoners dilemma can have cooperative outcome50Repeated GamesConclusionCooperation is difficult at best since these factors may change in the long runNeed a small number of firmsNeed stable demand and cost

40、conditionsThis could lead to price wars if dont have them51Oligopolistic Cooperationin the Water Meter IndustryCharacteristics of the MarketFour producers of water metersRockwell InternationalBadger MeterNeptune Water Meter CompanyHersey ProductsRockwell has about 35% of market shareBadger, Neptune,

41、 and Hersey combined have about a 50 to 55% share52Oligopolistic Cooperationin the Water Meter IndustryMost buyers are municipal water utilitiesVery inelastic demandNot a significant part of the budget for providing waterDemand is stableDemand grows steadily with populationUtilities have long-standi

42、ng relationships with suppliersReluctant to switch53Oligopolistic Cooperationin the Water Meter IndustrySignificant economies of scaleBoth long term relationship and economies of scale represent barriers to entryHard for new firms to enter marketIf firms were to cooperate, could earn significant mon

43、opoly profitsIf compete aggressively to gain market share, profits will fall to competitive levels54Oligopolistic Cooperationin the Water Meter IndustryThis is a Prisoners Dilemma what should the firms do?Lower price to a competitive levelCooperateCompanies have been playing repeated game for decade

44、sCooperation has prevailed given market characteristics55Sequential GamesPlayers move in turn, responding to each others actions and reactionsEx: Stackelberg model (ch. 12)Responding to a competitors ad campaignEntry decisionsResponding to regulatory policy56Sequential GamesGoing back to the product

45、 choice problemTwo new (sweet, crispy) cerealsSuccessful only if each firm produces one cerealSweet will sell betterBoth still profitable with only one producer57Modified Product Choice ProblemIf firms both announce their decisions independently and simultaneously, they will both pick sweet cereal a

46、nd both will lose moneyWhat if Firm 1 sped up production and introduced new cereal first?Now there is a sequential gameFirm 1 will think about what Firm 2 will do58Modified Product Choice ProblemFirm 1CrispySweetCrispySweetFirm 2-5, -510, 20-5, -520, 1059Extensive Form of a GameExtensive Form of a G

47、ameRepresentation of possible moves in a game in the form of a decision treeAllows one to work backward from the best outcome for Firm 160Product Choice Game in Extensive FormCrispySweetCrispySweet-5, -510, 2020, 10-5, -5Firm 1CrispySweetFirm 2Firm 261Sequential GamesThe Advantage of Moving FirstIn

48、this product-choice game, there is a clear advantage to moving firstThe first firm can choose a large level of output, thereby forcing second firm to choose a small levelCan show the firms mover advantage by revising the Stackelberg model and comparing to Cournot62First Mover AdvantageAssume: Duopol

49、y63First Mover AdvantageDuopoly64Choosing OutputFirm 17.5Firm 2112.50, 112.5056.25, 112.500, 0112.50, 56.25125, 93.7550, 7593.75, 12575, 50100, 10010157.5101565Choosing OutputThis payoff matrix illustrates various outcomesMove together, both produce 10If Firm 1 moves first (Q=15), best Firm 2 can do

50、 is 7.5Firm 17.5Firm 2112.50, 112.5056.25, 112.500, 0112.50, 56.25125, 93.7550, 7593.75, 12575, 50100, 10010157.5101566Threats, Commitments, and CredibilityStrategic MovesWhat actions can a firm take to gain advantage in the marketplace?Deter entryInduce competitors to reduce output, leave, raise pr

51、iceImplicit agreements that benefit one firm67Threats, Commitments, and CredibilityStrategic MoveAction that gives a player an advantage by constraining his behaviorFirm 1 must constrain his behavior to the extent Firm 2 is convinced that he is committed68Threats, Commitments, and CredibilityHow to

52、Make the First MoveDemonstrate CommitmentFirm 1 must do more than announce they will produce sweet cerealInvest in expensive advertising campaignBuy large order of sugar and send invoice to Firm 2Commitment must be enough to induce Firm 2 to make the decision Firm 1 wants it to make69Threats, Commit

53、ments, and CredibilityEmpty ThreatsIf a firm will be worse off if it charges a low price, the threat of a low price is not credible in the eyes of the competitorsWhen firms know the payoffs of each others actions, firms cannot make threats the other firm knows they will not followIn our example, Fir

54、m 1 will always charge high price and Firm 2 knows it70Pricing of Computers and Word ProcessorsFirm 1High PriceLow PriceHigh PriceLow PriceFirm 2100, 8080, 10010, 2020, 071Threats, Commitments, and CredibilitySometimes firms can make credible threatsScenarioRace Car Motors, Inc. (RCM) produces carsF

55、ar Out Engines (FOE) produces specialty car engines and sells most of them to RCMSequential game with RCM as the leaderFOE has no power to threaten to build big engines since RCM controls output72Production Choice ProblemFar Out EnginesSmall carsBig carsSmall enginesBig enginesRace Car Motors3, 63,

56、08, 31, 173Threats, Commitments, and CredibilityRCM does best by producing small carsKnows that Far Out will then produce small enginesFar Out prefers to make big enginesCan Far Out induce Race Car to produce big cars instead?74Threats, Commitments, and CredibilitySuppose Far Out threatens to produc

57、e big engines no matter what RCM does?Not credible since once RCM announces they are producing small cars, FOE will not have incentive to carry out threatCan make threat credible by altering pay off matrix by constraining its own choicesShutting down or destroying some small engine production capaci

58、ty75Modified Production Choice Problem0, 60, 08, 31, 1Far Out EnginesSmall carsBig carsSmall enginesBig enginesRace Car Motors76Modified Production Choice ProblemStrategic commitments can be effective but not without riskRely heavily on accurate knowledge of payoff matrix and industryMay have compet

59、itors out there that they dont know about and lose sales77Role of ReputationIf Far Out gets the reputation of being irrationalThey threaten to produce large engines no matter what Race Car doesThreat might be credible because irrational people dont always make profit maximizing decisionsA party thou

60、ght to be crazy can lead to a significant advantage78Bargaining StrategyBargaining situation can depend on ability to affect relative bargaining positionConsider two firms introducing one of two complementary goods:Firm 1 has cost advantage in Good AFirm 2 has cost advantage in Good B79Bargaining St