4.2.Strategies InExtensive Form Games.1.0(博弈论讲-Arizona State University).pdfVIP

Strategies in Extensive-Form Games Page 1 jim@ Jim Ratliff /gametheory Strategies in Extensive-Form Gamesù Recapitulation ____________________________________________________________________1 Strategy profiles of extensive-form games ______________________________________________2 The strategic form of an extensive-form game___________________________________________5 When Nature takes her turn at bat ____________________________________________________7 Randomized strategies in extensive-form games _________________________________________9 Behavior strategies _______________________________________________________________9 Mixed strategies_________________________________________________________________12 Mixed strategy § behavior strategy: the role of perfect recall _____________________________13 Mixed strategy § behavior strategy: computing the conditional probabilities _________________16 Behavior strategy § mixed strategy _________________________________________________18 Many mixed strategies give rise to the same distribution over outcomes ______________________19 Kuhn’s theorem: The equivalence of behavior and mixed strategies _________________________20 The restriction of a strategy to a subgame _____________________________________________21 Recapitulation We are now studying dynamic games—in which some decisions are made after others. We use the extensive form because it allows us to make explicit this temporal structure as well as to define the game’s information structure. (The results of previous decisions by one player may not be observable immediately, if ever, to her opponents.) We introduced the game tree as the supporting framework for the extensive form. Choices are made at decision nodes, which belong to the set X. One of these, viz. O, is designated the initial node, at which the game begins. It is assigned either to one of the players in the player set I={1,…,n} or to Nature; Nature would make a random choice representing any exogenous unce