5-10-2012Lecture 6:2I. Limits of Dominance SolvabilityA. Only one player with DSB. Neither has DSII. Nash EquilibriumA. Mutual Best ResponseB. No regretsC. Self-reinforcingIII. Coordination Games: Multiple EquilibriaA. AssuranceB. Battle of SexesC. “Focality”I. RoomiesColumn Clean MessT > R > P > S if the game is a Prisoner’s Dilemma5 > 3 > 1 > 0IA. Column Clean MessColumn Player has DS: messRow Player’s Best Response is to DSRow Player has a conscience Row Player would rather have 1 than 0 so the outcome is the same as in a PD.Changing one player doesn’t change the outcomes.“Normal Form”: matrices with payoffs for row and columnIB. / II.Column Clean MessCleanRowMessCleanRowMessCleanRow3350051133500211Nash Equilibrium: set of strategies, one for each player, such that no player can do better given the strategies of the other players*Nash Equilibria are not necessarily uniqueNO DS!Cooperation is possible in equilibrium but not guaranteedExistence of NE’s is bad for cooperatingThere can be more than one NE!IIIA.Assurance = “Stag Hunt”Would you rather go off on your own and hunt little rabbits or join the community on a stag hunt?Column Cooperate DefectCase 1: T > 3NE is defect, defectCase 2: T < 3NE 1 is cooperate, cooperateNE 2 is defect, defect“Multiple Equilibria” : not equivalent to numerous casesT > R > P > S : 3 separate things you have to look atRather than looking at these, ask yourself these two questions:1) Does each player have a dominant strategy?2) Do both players do worse from DS than if they both did the opposite?For the game above: 1) Yes if T > 3 2) Yes→PDIIIB. CooperateRowDefect3NE320021NE133T00T1NE1Battle of Sexes = Primary ElectionsRow player’s decision only affects the row!Column Player can only choose column!Him Ballet Ball gameBoth players have regrets at: 0,0 -1, -1IIIC. HockeyColumn Helmets NotWhich equilibrium is focal?This depends on people’s expectations based on culture, tradition, etcChange will not happen on its ownPD: depends on payoffs in relation to anotherNE: given what other did, did I do best?If yes, then NE!BalletHerBall