Chapter 9 - Game theory and strategic thinking. In this chapter you will learn: What strategic behavior is and what the components of a strategic game are, why noncooperation is a dominant strategy in the prisoners’ dilemma, how repeated play can enable cooperation,...
Chapter9 GameTheoryandStrategicThinking â2014byMcGrawHillEducation Whatwillyoulearninthischapter? ã Whatstrategicbehaviorisandwhatthe componentsofastrategicgameare ã Whynoncooperationisadominantstrategyinthe prisoners’ dilemma • How repeated play can enable cooperation • How backward induction can be used to make decisions • How first‐movers have an advantage • How patient players have more bargaining power • How a commitment strategy can allow players to achieve their goals by limiting their options © 2014 by McGraw‐Hill Education Games and strategic behavior • People behave rationally when they look at the trade‐offs they face and pursue their goals in the most effective way possible • Game theory studies how people behave strategically under different circumstances – A game refers to any situation involving at least two people that requires those involved to think strategically – Behaving strategically involves acting to achieve a goal byanticipatingtheinterplaybetweenyourownand othersdecisions â2014byMcGrawHillEducation Rules,strategies,andpayoffs ã Allgamessharethreefeatures:rules, strategies,andpayoffs Rules define the actions that are allowed in a game – Strategies are the plans of action that players follow to achieve their goals. – Payoffs are the rewards that come from particular actions © 2014 by McGraw‐Hill Education The prisoners’ dilemma The prisoners’ dilemma is a one‐time game of strategy in which two people in isolation make the choice to ‘confess’ or ‘don’t confess’ that together they committed a crime • Payoff depends on actions of both players: You Confess Don’t confess Your accomplice Confess Don’t confess 10 years 3rd choice 10 years 3rd choice 20 years 4th choice year 1st choice years 2nd choice year 1st choice 20 years 4th choice years 2nd choice – Both confess – One player confesses – Neither player confesses • Solve game by finding what the other player would do if you choose a specific action and vice‐versa • Because of strategic behavior, the realized outcome is not the best possible outcome available © 2014 by McGraw‐Hill Education The prisoners’ dilemma The prisoners’ dilemma can be extended to other applications, such as the Bush‐Kerry presidential election and the choice to use negative or positive advertising Kerry Go negative Stay positive Bush Go negative Tight race Bad reputation 3rd choice Tight race Bad reputation 3rd choice Win 1st choice Lose 4th choice © 2014 by McGraw‐Hill Education Stay positive Lose 4th choice Win 1st choice Tight race Good reputation 2nd choice Tight race Good reputation 2nd choice • Does either player have a dominant strategy – an action that they always choose? – Kerry: Go negative – Bush: Go negative • The dominant strategies solve the game • The realized outcome is not the best possible outcome available – This is due to an inability to cooperate The prisoners’ dilemma The prisoners’ dilemma can also be extended to whether you should or should not litter You Don’t litter Litter Don’t litter Yourneighbor Litter -10 3rd choice -15 4th choice 1st choice -10 3rd choice 1st choice -5 2nd choice -5 2nd choice -15 4th choice • Sometimes all players lose, but want to contain their losses • The dominant strategies solve thegame ã Thesolutiontothegameis calledaNashequilibrium whenallplayerschoosethe beststrategytheycangiven thechoicesofallother players â2014byMcGrawHillEducation Dominant strategies While dominant strategies can sometimes solve for the Nash equilibrium, sometimes games do not have an equilibrium Scissors Paper Player A Rock Player B Rock Paper Scissors Tie B wins A wins A wins Tie B wins B wins A wins Tie • The game of rock, paper, scissors has no Nash equilibrium • There is no stable outcome where you or your opponent would wish to change your strategy once youfindoutwhatthe otherplayerisdoing â2014byMcGrawHillEducation Reachingequilibrium ã TheNashequilibriumissometimesreferredto asthenoncooperativeequilibrium Thisisbecauseplayersactindependently,only pursuingtheirindividualinterests ã Sometimesplayersmaycollude(orcooperate) toobtainabetteroutcomeforboth Inthecaseoftheprisonersdilemma,the cooperativeequilibriumwouldmakebothplayers betteroff â2014byMcGrawHillEducation Active Learning: Finding equilibrium Suppose Greg and Renee must choose whether or not to offer a lunch special at their respective restaurants • Find the Nash equilibrium Offer lunch special Don’t offer lunch special Renee’s Greek Salad Bar Greg’s Pizzeria Don’t offer lunch special Offer lunch special -10 -15 20 -5 30 -10 35 25 â2014byMcGrawHillEducation 10 Avoidingcompetitionthroughcommitment ã Sustainingcollusiontoobtainthecooperative equilibriumisextremelydifficult,asoneplayer can typically be made better off by defecting • It may require a punishment for defecting that is larger than the payoff for defecting – An agreement to submit to a penalty for defecting to obtain a certain outcome is an example of a commitment strategy • Often the commitment is non‐binding and individualsbreaktheiragreement â2014byMcGrawHillEducation 11 Promotingcompetitioninthepublicinterest Whilecooperationmayservethebestinterestsofthe playersdirectlyinvolved,itmayhavesocietal consequences ã Supposeasmalltownhas twogasstations,each setting their price Competition Exxon High prices Low prices Conoco Low prices Low profits 3rd choice Low profits 3rd choice High profits 1st choice No profit 4th choice High prices – If they collude, they will earn moderate profits – If they compete, they will earn low profits No profit 4th choice High profits 1st choice Moderate profits 2nd choice Moderate profits 2nd choice • The non‐cooperative Nash equilibrium is the competitive equilibrium Collusion © 2014 by McGraw‐Hill Education 12 Repeat play in the prisoners’ dilemma • Repeatedgamesarenotonetime,butare playedmorethanonce ã Thecooperativeequilibriumismorelikelyto occurbecausesimplecommitment mechanismsexist Titfortat:Oneplayerdoesthesameactionasthe otherdidinthepreviousgame â2014byMcGrawHillEducation 13 Sequential games • In all of the previously discussed games, both players moved simultaneously • In many instances, an individual or company must move prior to other participants choosing an action – Typicallytheplayerwhochoosesfirstgetsahigher payoff,afirstmoveradvantage ã Theoptimalstrategiesaredeterminedbyusing backwardinduction,inwhichtheoptimalstrategy ofthelastplayertochooseisdetermined, followedbythesecondtolastplayer,andsoon â2014byMcGrawHillEducation 14 Sequentialgames • Suppose you aspire to win the Pulitzer Prize • Start with the outcome and work backwards to determine your sequence of choices Q. What do you have to do to win the Pulitzer prize? A. You have to work for a top newspaper Q. What do you have to do to get a job at a top newspaper? A. You have to have a graduate degree in journalism Q. What do you have to do to get a graduate degree in journalism? A.YouhavetohaveanundergraduatedegreeinEnglish Q.Whatdoyouhavetodotogetthatdegree? A.Youhavetotaketheprerequisitecoursesinnonfictionwriting Therefore,youshouldtakeintroductorynonfictionwritingnextsemester â2014byMcGrawHillEducation 15 Deterringmarketentry:asequentialgame ã Adecisiontreevisualizessequentialgames.Forexample, McDonald’s is considering a new store in a small town • Profits (the payoffs) are affected by what location is built in and by how many burger joints enter Profits Outskirts Center of town Burger King: Burger King: Should we enter? Should we enter? If so, where? If so, where? Center Outskirts Outskirts of town Burger King: Bu ger King: Shoul we e ter? Should we enter? If so whe e? If so, where? Center No â2014byMcGrawHillEducation BK:4% McD:4% ã No McDonalds: Whereshouldwe build? ã BK: 2% McD: 12% BK: 10% McD: 12% BK: 8% McD: 8% • BK: 12% McD: 2% • BK: 10% McD: 20% If McD enters in the center of town: – BK will not enter and earns a 10% return – McD earns 12% return If McD enters in outskirts of town: – BK will enter at center and earns a 12% return – McD earns 2% return McD chooses between 12% return or 2% return McD chooses to locate at the center of town and BK does not enter 16 Sequential games • First‐mover advantage can be extremely important in one‐round sequential games • Consider a bargaining game, in which a company is negotiating with its employees’ labor union over wages Share of surplus 1% surplus Company: What Company:What should wewepay pay should employees? employees? Yes Labor Union: Should we accept the new offer? No Company: 99% Union: 1% Company: 0% Union: 0% • If this was a one‐round game and the company moved first, it could offer just 1 percent of the surplus and the union would have to make a choice: • The union chooses between a 1% pay raise and 0% • This is an example of an ultimatum game: One player makes an offer and the other player has the simple choice of whether to accept or reject – – – Accept the offer Reject it by going on strike and shutting down production Theunionwillaccepttheoffer â2014byMcGrawHillEducation 17 Commitmentinsequentialgames ã Commitmentinsequentialgamescanaffecttherealized outcome ã SupposethattheAztecsandCortesmenhavethechoiceto eitheradvanceorretreat • Result Advance Advance Cortés: Advance or retreat? Advance Retreat Cortộs: Advance or retreat? Retreat â2014byMcGrawHillEducation ã Retreat Aztecs: Advance or retreat? Cortés: fight to death Aztecs: fight to death Both prefer land, lives, and then a fight to the death If all strategies are available: Cortés: lives Aztecs: keep land Cortés: wins land Aztecs: live Cortés: lives Aztecs: keep land – • If Aztecs advance, Cortes will retreat If Aztecs retreat, Cortes will advance Given these strategies, Aztecs will advance and Cortes will retreat 18 Commitment in sequential games • Consider the same game, but now assume that Cortes commits to advancing by burning his ships Result Advance Advance Cortés: Advance or retreat? • Retreat Aztecs: Advance or retreat? Retreat • Cortés: fight to death Aztecs: fight to death Eliminated – Advance Cortés: wins land Aztecs: live Cortés: Advance or retreat? Burning his ships eliminates the choice to retreat Given this limited choice set, Aztecs choose between: – Retreat Eliminated ã Advancing,andfightingto thedeath Retreating,andliving Giventhesestrategies, Aztecswillretreatand Corteswilladvance â2014byMcGrawHillEducation 19 Active Learning: Commitment in sequential games In an effort to not lose market share, suppose Burger King commits to build in every new town that McDonalds does • How does this affect the outcome? Profits Outskirts Center of town Burger King: Burger King: Should we enter? Should we enter? If so, where? If so, where? No McDonalds: Where should we build? Outskirts of town Center Outskirts Burger King: Bu ger King: Shoul we e ter? Should we enter? If so whe e? If so, where? Center No BK: 2% McD: 12% BK: 4% McD: 4% BK: 10% McD: 12% BK: 8% McD: 8% BK: 12% McD: 2% BK: 10% McD: 20% © 2014 by McGraw‐Hill Education 20 Summary • The concept of strategic games was introduced • Many real‐life decisions can be analyzed as if a strategic game is being played • Game theory can explain choices that may seemunintuitive,suchaswhypeoplein custodyconfesstotheircrimes ã Simultaneousmovegameswereexaminedas wellassequentialmovegames Commitmentcanaffecttheoutcomeofboth â2014byMcGrawHillEducation 21 ... Don’t litter Litter Don’t litter Yourneighbor Litter -1 0 3rd choice -1 5 4th choice 1st choice -1 0 3rd choice 1st choice -5 2nd choice -5 2nd choice -1 5 4th choice • Sometimes all players lose, but want to contain their ... â2014byMcGrawHillEducation 20 Summary ã Theconceptofstrategicgameswas introduced • Many real‐life decisions can be analyzed as if a strategic? ?game? ?is being played • Game? ?theory? ?can explain choices that may ... Both prefer land, lives, and? ?then a fight to the death If all strategies are available: Cortés: lives Aztecs: keep land Cortés: wins land Aztecs: live Cortés: lives Aztecs: keep land – • If Aztecs advance, Cortes