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Lecture 12June 4, 20031Dynamic Games of Complete InformationChapter 2Subgame-Perfect Nash EquilibriumOutline of dynamic games of complete informationDynamic games of complete information Extensive-form representationDynamic games of complete and perfect informationGame treeSubgame-perfect Nash equilibrium2Backward inductionApplicationsDynamic games of complete and imperfect informationMore applicationsRepeated games2.1. Dynamic games of complete and perfect informationExample: Entry Game:An incumbent monopolistfaces the possibility of entry by a challenger.The challengermay choose to enterorstay out.If the challengerenters, the incumbentcan choose either to accommodateor to fight.The payoffs are common knowledge.3ChallengerInOutIncumbentAF1, 22, 10, 0The first numberis the payoff of the challenger. The second numberis the payoff of the incumbent.Sequential-move matching penniesEach of the two players has a penny. Player 1 first chooses whether to show the Head or the Tail. After observing player 1’s choice, player 2 chooses Player 1Player 2HTPlayer 24to show Head or TailBoth players know the following rules:If two pennies match (both heads or both tails) then player 2 wins player 1’s penny. Otherwise, player 1 wins player 2’s penny. HT-1, 11, -1HT1, -1-1, 1Dynamic (or sequential-move) games of complete informationA set of playersWho moves when and what action choices are available?What do players know when they move?5Players’ payoffs are determined by their choices.All these are common knowledge among the players.Definition: extensive-form representationThe extensive-form representation of a game specifies: the players in the gamewhen each player has the movewhat each player can do at each of his or6what each player can do at each of his or her opportunities to movewhat each player knows at each of his or her opportunities to movethe payoff received by each player depend on each combination of moves that could be chosen by the players
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