国外博弈论课件lecture3.ppt

May 21, 2003 73-347 Game Theory--Lecture 3 May 21, 2003 Lecture 3 Static (or Simultaneous-Move) Games of Complete Information Nash Equilibrium Best Response Function Outline of Static Games of Complete Information Introduction to games Normal-form (or strategic-form) representation Iterated elimination of strictly dominated strategies Nash equilibrium Review of concave functions, optimization Applications of Nash equilibrium Mixed strategy Nash equilibrium Today’s Agenda Review of previous classes Nash equilibrium Best response function Use best response function to find Nash equilibria Examples Review The normal-form (or strategic-form) representation of a game G specifies: A finite set of players {1, 2, ..., n}, players’ strategy spaces S1 S2 ... Sn and their payoff functions u1 u2 ... un where ui : S1 × S2 × ...× Sn→R. Review Static (or simultaneous-move) game of complete information Each player’s strategies and payoff function are common knowledge among all the players. Each player i chooses his/her strategy si without knowledge of others’ choices. Then each player i receives his/her payoff ui(s1, s2, ..., sn). The game ends. Definition: strictly dominated strategy Review: iterated elimination of strictly dominated strategies If a strategy is strictly dominated, eliminate it The size and complexity of the game is reduced Eliminate any strictly dominated strategies from the reduced game Continue doing so successively Iterated elimination of strictly dominated strategies: an example New solution concept: Nash equilibrium The combination of strategies (B’, R’) has the following property: Player 1 CANNOT do better by choosing a strategy different from B’, given that player 2 chooses R’. Player 2 CANNOT do better by choosing a strategy different from R’, given that player 1 chooses B’. (B’, R’) is called a Nash equilibrium Nash Equilibrium: idea Nash equilibrium A set of strategies, one for each player, such that each player’s strategy is best for her,