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Chapter 13Game Theory and Competitive Strategy2005 Pearson Education,Inc.2Topics to be DiscussedlGaming and Strategic DecisionslDominant StrategieslThe Nash Equilibrium RevisitedlRepeated Games2005 Pearson Education,Inc.3Topics to be DiscussedlSequential GameslThreats,Commitments,and CredibilitylEntry DeterrencelBargaining StrategylAuctions2005 Pearson Education,Inc.4Gaming and Strategic DecisionslGame is any situation in which players(the participants)make strategic decisionsmEx:firms competing with each other by setting prices,group of consumers bidding against each other in an auctionlStrategic decisions result in payoffs to the players:outcomes that generate rewards or benefits2005 Pearson Education,Inc.5Gaming and Strategic DecisionslGame theory tries to determine optimal strategy for each playerlStrategy is a rule or plan of action for playing the gamelOptimal strategy for a player is one that maximizes the expected payofflWe consider players who are rational they think through their actions2005 Pearson Education,Inc.6Gaming and Strategic Decisionsl“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)2005 Pearson Education,Inc.7Noncooperative vs.Cooperative GameslCooperative GamemPlayers negotiate binding contracts that allow them to plan joint strategieslExample:Buyer and seller negotiating the price of a good or service or a joint venture by two firms(i.e.,Microsoft and Apple)lBinding contracts are possible2005 Pearson Education,Inc.8Noncooperative vs.Cooperative GameslNoncooperative GamemNegotiation and enforcement of binding contracts between players is not possiblelExample:Two competing firms,assuming the others behavior,independently determine pricing and advertising strategy to gain market sharelBinding contracts are not possible2005 Pearson Education,Inc.9Noncooperative vs.Cooperative Gamesl“The strategy design is based on understanding your 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)2005 Pearson Education,Inc.10Gaming and Strategic DecisionslAn Example:How to buy a dollar billlAuction a dollar billlHighest bidder receives the dollar in return for the amount bidlSecond highest bidder must pay the amount he or she bid but gets nothing in returnlHow much would you bid for a dollar?1.Typically bid more for the dollar when faced with loss as second highest bidder2005 Pearson Education,Inc.11Acquiring a CompanylScenariomCompany A:The AcquirermCompany T:The TargetmA will offer cash for all of Ts shareslThe value and viability of T depends on the outcome of a current oil exploration project2005 Pearson Education,Inc.12Acquiring a CompanylProject failure:Ts value=$0lProject success:Ts value=$100/sharelAll outcomes in between equally likelylTs value will be 50%greater with As management2005 Pearson Education,Inc.13Acquiring a CompanylScenariomA must submit the proposal before the exploration outcome is knownmT will not choose to accept or reject until after the outcome is known only to TmCompany T will accept any offer that is greater than the per share value of the company under current managementlHow much should A offer?2005 Pearson Education,Inc.14Dominant StrategieslDominant Strategy is one that is optimal no matter what an opponent doesmAn ExamplelA and B sell competing productslThey are deciding whether to undertake advertising campaigns2005 Pearson Education,Inc.15Payoff Matrix for Advertising GameFirm AAdvertiseDontAdvertiseAdvertiseDontAdvertiseFirm B10,515,010,26,82005 Pearson Education,Inc.16Payoff Matrix for Advertising Gamel ObservationsmA:regardless of B,advertising is the bestmB:regardless of A,advertising is bestFirm AAdvertiseDontAdvertiseAdvertiseDontAdvertiseFirm B10,515,010,26,82005 Pearson Education,Inc.17Payoff Matrix for Advertising Gamel ObservationsmDominant strategy for A and B is to advertisemDo not worry about the other playermEquilibrium in dominant strategyFirm AAdvertiseDontAdvertiseAdvertiseDontAdvertiseFirm B10,515,010,26,82005 Pearson Education,Inc.18Dominant StrategieslEquilibrium in dominant strategiesmOutcome of a game in which each firm is doing the best it can regardless of what its competitors are doingmOptimal strategy is determined without worrying about the actions of other playerslHowever,not every game has a dominant strategy for each player2005 Pearson Education,Inc.19Dominant StrategieslGame Without Dominant StrategymThe optimal decision of a player without a dominant strategy will depend on what the other player doesmRevising the payoff matrix,we can see a situation where no dominant strategy exists2005 Pearson Education,Inc.2010,515,020,26,8Firm AAdvertiseDontAdvertiseAdvertiseDontAdvertiseFirm BModified Advertising Game2005 Pearson Education,Inc.2110,515,020,26,8Firm AAdvertiseDontAdvertiseAdvertiseDontAdvertiseFirm BModified Advertising Gamel ObservationsmA:No dominant strategy;depends on Bs actionsmB:Dominant strategy is to advertisemFirm A determines Bs dominant strategy and makes its decision accordingly2005 Pearson Education,Inc.22The Nash Equilibrium RevisitedlA dominant strategy is stable,but in many games one or more party does not have a dominant strategylA more general equilibrium concept is the Nash Equilibrium introduced in Chapter 12mA set of strategies(or actions)such that each player is doing the best it can given the actions of its opponents2005 Pearson Education,Inc.23The Nash Equilibrium RevisitedlNone of the players have incentive to deviate from its Nash strategy,therefore it is stablemIn the Cournot model,each firm sets its own price assuming the other firms outputs are fixed.Cournot equilibrium is a Nash Equilibrium.2005 Pearson Education,Inc.24The Nash Equilibrium RevisitedlDominant Strategym“Im doing the best I can no matter what you do.Youre doing the best you can no matter what I do.”lNash Equilibriumm“Im doing the best I can given what you are doing.Youre doing the best you can given what I am doing.”lDominant strategy is a special case of Nash equilibrium2005 Pearson Education,Inc.25The Nash Equilibrium Revisitedl Two cereal companies face a market in which two new types of cereal can be successfully introduced,provided each type is introduced by only one firml Product Choice ProblemmMarket for one producer of crispy cerealmMarket for one producer of sweet cerealmEach firm only has the resources to introduce one cerealmNoncooperative2005 Pearson Education,Inc.26Product Choice ProblemFirm 1CrispySweetCrispySweetFirm 2-5,-510,10-5,-510,102005 Pearson Education,Inc.27Product Choice ProblemFirm 1CrispySweetCrispySweetFirm 2-5,-510,10-5,-510,10l If Firm 1 hears Firm 2 is introducing a new sweet cereal,its best action is to make crispyl Bottom left corner is Nash equilibriuml What is other Nash Equilibrium?2005 Pearson Education,Inc.28Beach Location GamelScenariomTwo competitors,Y and C,selling soft drinksmBeach is 200 yards longmSunbathers are spread evenly along the beachmPrice Y=Price CmCustomer will buy from the closest vendor2005 Pearson Education,Inc.29Beach Location GamelWhere will the competitors locate(i.e.,where is the Nash equilibrium)?lWill want to all locate in center of beachmSimilar to groups of gas stations,car dealerships,etc.Ocean0BBeachA200 yardsC2005 Pearson Education,Inc.30The Nash Equilibrium RevisitedlMaximin Strategies-ScenariomTwo firms compete selling file encryption softwaremThey both use the same encryption standard(files encrypted by one software can be read by the other-advantage to consumers)mFirm 1 has a much larger market share than Firm 2mBoth are considering investing in a new encryption standard2005 Pearson Education,Inc.31Maximin StrategyFirm 1Dont investInvestFirm 20,0-10,1020,10-100,0Dont investInvest2005 Pearson Education,Inc.32Maximin StrategyFirm 1Dont investInvestFirm 20,0-10,1020,10-100,0Dont investInvestl ObservationsmDominant strategy Firm 2:InvestmFirm 1 should expect Firm 2 to investmNash equilibriumlFirm 1:investlFirm 2:InvestmThis assumes Firm 2 understands the game and is rational2005 Pearson Education,Inc.33Maximin StrategyFirm 1Dont investInvestFirm 20,0-10,1020,10-100,0Dont investInvestl ObservationsmIf Firm 2 does not invest,Firm 1 incurs significant lossesmFirm 1 might play dont investlMinimize losses to 10 maximin strategy2005 Pearson Education,Inc.34Maximin StrategylIf both are rational and informedmBoth firms investmNash equilibriumlIf Player 2 is not rational or completely informedmFirm 1s maximin strategy is to not investmFirm 2s maximin strategy is to investmIf 1 knows 2 is using a maximin strategy,1 would invest2005 Pearson Education,Inc.35Maximin StrategylIf Firm 1 is unsure about what Firm 2 will do,it can assign probabilities to each possible actionmCould use a strategy that maximizes its expected payoffmFirm 1s strategy depends critically on its assessment of probabilities for Firm 22005 Pearson Education,Inc.36Prisoners DilemmaPrisoner AConfessDont ConfessConfessDontConfessPrisoner B-5,-5-1,-10-2,-2-10,-12005 Pearson Education,Inc.37Prisoners DilemmaPrisoner AConfessDont ConfessConfessDontConfessPrisoner B-5,-5-1,-10-2,-2-10,-1l What is the:mDominant strategymNash equilibriummMaximin solutionl Dominant strategies are also maximin strategiesl Both confess is both Nash equilibrium and maximin solution2005 Pearson Education,Inc.38Mixed StrategylPure StrategymPlayer makes a specific choice or takes a specific actionlMixed StrategymPlayer makes a random choice among two or more possible actions,based on a set of chosen probabilities2005 Pearson Education,Inc.39Matching PenniesPlayer AHeadsTailsHeadsTailsPlayer B1,-1-1,11,-1-1,12005 Pearson Education,Inc.40Matching Penniesl Pure strategy:No Nash equilibriummNo combination of head and tails leaves both players better offl Mixed strategy:Random choice is a Nash equilibriumPlayer AHeadsTailsHeadsTailsPlayer B1,-1-1,11,-1-1,12005 Pearson Education,Inc.41Matching PennieslPlayer A might flip coin playing heads with probability and tails with probabilitylIf both players follow this strategy,there is a Nash equilibrium both players will be doing the best they can given what their opponent is doinglAlthough the outcome is random,the expected payoff is 0 for each player2005 Pearson Education,Inc.42Mixed StrategylOne reason to consider mixed strategies is when there is a game that does not have any Nash equilibriums in pure strategylWhen allowing for mixed strategies,every game has a Nash equilibriumlMixed strategies are popular for games like pokerlA firm might not find it reasonable2005 Pearson Education,Inc.43The Battle of the SexesJimWrestlingOperaWrestlingOperaJoan2,10,01,20,02005 Pearson Education,Inc.44The Battle of the Sexesl Pure StrategymBoth watch wrestlingmBoth watch operal Mixed StrategymJim chooses wrestlingmJoan chooses wrestlingJim WrestlingOperaWrestlingOperaJoan2,10,01,20,02005 Pearson Education,Inc.45Repeated GameslGame in which actions are taken and payoffs are received over and over againlOligopolistic firms play a repeated gamelWith each repetition of the Prisoners Dilemma,firms can develop reputations about their behavior and study the behavior of their competitors2005 Pearson Education,Inc.46Pricing ProblemFirm 1Low PriceHigh PriceLow PriceHigh PriceFirm 210,10100,-5050,50-50,1002005 Pearson Education,Inc.47Pricing ProblemlHow does a firm find a strategy that would work best on average against all or almost all other strategies?lTit-for-tat strategymRepeated game strategy in which a player responds in kind to an opponents previous play,cooperating with cooperative opponents and retaliating against uncooperative ones2005 Pearson Education,Inc.48Tit-for-Tat StrategylWhat if the game is infinitely repeated?mCompetitors repeatedly set price every month,forevermTit-for-tat strategy is rationallIf competitor charges low price and undercuts firmlWill get high profits that month but know I will lower price next monthlBoth of us will get lower profits if keep undercutting,so not rational to undercut2005 Pearson Education,Inc.49Tit-for-Tat Strategyl What if repeated a finite number of times?mIf both firms are rational,they will charge high prices until the last monthmAfter the last month,there is no retaliation possiblemBut in the month before last month,knowing that will charge low price in last month,will charge low price in month beforemKeep going and see that only rational outcome is for both firms to charge low price every month2005 Pearson Education,Inc.50Tit-for-Tat StrategylIf firms dont believe their competitors are rational or think perhaps they arent,cooperative behavior is a good strategylMost managers dont know how long they will be competing with their rivalslIn a repeated game,prisoners dilemma can have cooperative outcome2005 Pearson Education,Inc.51Repeated GameslConclusionmCooperation is difficult at best since these factors may change in the long runmNeed a small number of firmsmNeed stable demand and cost conditionslThis could lead to price wars if dont have them2005 Pearson Education,Inc.52Oligopolistic Cooperationin the Water Meter IndustrylCharacteristics of the MarketmFour producers of water meterslRockwell InternationallBadger MeterlNeptune Water Meter CompanylHersey ProductslRockwell has about 35%of market sharelBadger,Neptune,and Hersey combined have about a 50 to 55%share2005 Pearson Education,Inc.53Oligopolistic Cooperationin the Water Meter IndustrylMost buyers are municipal water utilitieslVery inelastic demandmNot a significant part of the budget for providing waterlDemand is stablemDemand grows steadily with populationlUtilities have long-standing relationships with suppliersmReluctant to switch2005 Pearson Education,Inc.54Oligopolistic Cooperationin the Water Meter IndustrylSignificant economies of scalelBoth long term relationship and economies of scale represent barriers to entrymHard for new firms to enter marketlIf firms were to cooperate,could earn significant monopoly profitslIf compete aggressively to gain market share,profits will fall to competitive levels2005 Pearson Education,Inc.55Oligopolistic Cooperationin the Water Meter IndustrylThis is a Prisoners Dilemma what should the firms do?mLower price to a competitive levelmCooperatelCompanies have been playing repeated game for decadeslCooperation has prevailed given market characteristics2005 Pearson Education,Inc.56Sequential GameslPlayers move in turn,responding to each others actions and reactionsmEx:Stackelberg model(ch.12)mResponding to a competitors ad campaignmEntry decisionsmResponding to regulatory policy2005 Pearson Education,Inc.57Sequential GameslGoing back to the product choice problemmTwo new(sweet,crispy)cerealsmSuccessful only if each firm produces one cerealmSweet will sell bettermBoth still profitable with only one producer2005 Pearson Education,Inc.58Modified Product Choice ProblemlIf firms both announce their decisions independently and simultaneously,they will both pick sweet cereal and both will lose moneylWhat if Firm 1 sped up production and introduced new cereal first?mNow there is a sequential gamemFirm 1 will think about what Firm 2 will do2005 Pearson Education,Inc.59Modified Product Choice ProblemFirm 1CrispySweetCrispySweetFirm 2-5,-510,20-5,-520,102005 Pearson Education,Inc.60Extensive Form of a Gamel Extensive Form of a GamemRepresentation of possible moves in a game in the form of a decision treelAllows one to work backward from the best outcome for Firm 12005 Pearson Education,Inc.61Product Choice Game in Extensive FormCrispySweetCrispySweet-5,-510,2020,10-5,-5Firm 1CrispySweetFirm 2Firm 22005 Pearson Education,Inc.62Sequential GameslThe Advantage of Moving FirstmIn this product-choice game,there is a clear advantage to moving firstmThe first firm can choose a large level of output,thereby forcing second firm to choose a small levelmCan show the firms mover advantage by revising the Stackelberg model and comparing to Cournot2005 Pearson Education,Inc.63First Mover AdvantagelAssume:DuopolyFirm and Production Total/1001010:0302121 PQQCournotMCQQ QQP2005 Pearson Education,Inc.64First Mover AdvantagelDuopoly25.56 50.112 50.7 and 5.7 15 rg)(StackelbeFirst Moves FirmFirm/50.112 15 and 5.7 CollusionWith 212121PQQPQQ2005 Pearson Education,Inc.65Choosing OutputFirm 17.5Firm 2112.50,112.5056.25,112.500,0112.50,56.25125,93.7550,7593.75,12575,50100,10010157.510152005 Pearson Education,Inc.66Choosing Outputl This payoff matrix illustrates various outcomesmMove together,both produce 10mIf Firm 1 moves first(Q=15),best Firm 2 can do is 7.5Firm 17.5Firm 2112.50,112.5056.25,112.500,0112.50,56.25125,93.7550,7593.75,12575,50100,10010157.510152005 Pearson Education,Inc.67Threats,Commitments,and CredibilitylStrategic MovesmWhat actions can a firm take to gain advantage in the marketplace?lDeter entrylInduce competitors to reduce output,leave,raise pricelImplicit agreements that benefit one firm2005 Pearson Education,Inc.68Threats,Commitments,and CredibilitylStrategic MovemAction that gives a player an advantage by constraining his behaviormFirm 1 must constrain his behavior to the extent Firm 2 is convinced that he is committed2005 Pearson Education,Inc.69Threats,Commitments,and CredibilitylHow to Make the First MovemDemonstrate CommitmentmFirm 1 must do more than announce they will produce sweet cereallInvest in expensive advertising campaignlBuy large order of sugar and send invoice to Firm 2mCommitment must be enough to induce Firm 2 to make the decision Firm 1 wants it to make2005 Pearson Education,Inc.70Threats,Commitments,and CredibilitylEmpty ThreatsmIf 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 competitorsmWhen firms know the payoffs of each others actions,firms cannot make threats the other firm knows they will not followmIn our example,Firm 1 will always charge high price and Firm 2 knows it2005 Pearson Education,Inc.71Pricing of Computers and Word ProcessorsFirm 1High PriceLow PriceHigh PriceLow PriceFirm 2100,8080,10010,2020,02005 Pearson Education,Inc.72Threats,Commitments,and CredibilitylSometimes firms can make credible threatslScenariomRace Car Motors,Inc.(RCM)produces carsmFar Out Engines(FOE)produces specialty car engines and sells most of them to RCMmSequential game with RCM as the leadermFOE has no power to threaten to build big engines since RCM controls output2005 Pearson Education,Inc.73Production Choice ProblemFar Out EnginesSmall carsBig carsSmall enginesBig enginesRace Car Motors3,63,08,31,12005 Pearson Education,Inc.74Threats,Commitments,and CredibilitylRCM does best by producing small carslKnows that Far Out will then produce small engineslFar Out prefers to make big engineslCan Far Out induce Race Car to produce big cars instead?2005 Pearson Education,Inc.75Threats,Commitments,and CredibilitylSuppose Far Out threatens to produce big engines no matter what RCM does?mNot credible since once RCM announces they are producing small cars,FOE will not have incentive to carry out threatmCan make threat credible by altering pay off matrix by constraining its own choiceslShutting down or destroying some small engine production capacity2005 Pearson Education,Inc.76Modified Production Choice Problem0,60,08,31,1Far Out EnginesSmall carsBig carsSmall enginesBig enginesRace Car Motors2005 Pearson Education,Inc.77Modified Production Choice ProblemlStrategic commitments can be effective but not without riskmRely heavily on accurate knowledge of payoff matrix and industrymMay have competitors out there that they dont know about and lose sales2005 Pearson Education,Inc.78Role of ReputationlIf Far Out gets the reputation of being irrationalmThey threaten to produce large engines no matter what Race Car doeslThreat might be credible because irrational people dont always make profit maximizing decisionslA party thoug
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