国外博弈论课件lecture15.ppt

June 10, 2003 73-347 Game Theory--Lecture 15 June 10, 2003 Lecture 15 Dynamic Games of Complete Information Dynamic Games of Complete and Perfect Information Outline of dynamic games of complete information Dynamic games of complete information Extensive-form representation Dynamic games of complete and perfect information Game tree Subgame-perfect Nash equilibrium Backward induction Applications Dynamic games of complete and imperfect information More applications Repeated games Today’s Agenda Review of previous class Subgame-perfect Nash equilibrium Backward induction Stackelberg’s model of duopoly (2.1.B of Gibbons, 6.2 of Osborne) Sequential-move Bertrand model of duopoly (differentiated products) Dynamic games of complete and perfect information Perfect information All previous moves are observed before the next move is chosen. A player knows Who has moved What before she makes a decision Strategy and payoff A strategy for a player is a complete plan of actions. It specifies a feasible action for the player in every contingency in which the player might be called on to act. It specifies what the player does at each of her nodes Nash equilibrium in a dynamic game We can also use normal-form to represent a dynamic game The set of Nash equilibria in a dynamic game of complete information is the set of Nash equilibria of its normal-form How to find the Nash equilibria in a dynamic game of complete information Construct the normal-form of the dynamic game of complete information Find the Nash equilibria in the normal-form Subgame-perfect Nash equilibrium A Nash equilibrium of a dynamic game is subgame-perfect if the strategies of the Nash equilibrium constitute or induce a Nash equilibrium in every subgame of the game. Subgame-perfect Nash equilibrium is a Nash equilibrium. Subgame A subgame of a game tree begins at a nonterminal node and includes all the nodes and edges following the nonterminal node A subgame beginning at a nonterminal node x can be obtained