国外博弈论课件lecture7.ppt

May 28, 2003 73-347 Game Theory--Lecture 7 May 28, 2003 Lecture 7 Static (or Simultaneous-Move) Games of Complete Information Mixed Strategy Nash Equilibrium 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 class Mixed strategies Mixed strategy Nash equilibrium Use best response to find mixed strategy Nash equilibrium Matching pennies Head is Player 1’s best response to Player 2’s strategy Tail Tail is Player 2’s best response to Player 1’s strategy Tail Tail is Player 1’s best response to Player 2’s strategy Head Head is Player 2’s best response to Player 1’s strategy Head Hence, NO Nash equilibrium Solving matching pennies Randomize your strategies to surprise the rival Player 1 chooses Head and Tail with probabilities r and 1-r, respectively. Player 2 chooses Head and Tail with probabilities q and 1-q, respectively. Mixed Strategy: Specifies that an actual move be chosen randomly from the set of pure strategies with some specific probabilities. Solving matching pennies Player 1’s best responseB1(q): Head (r=1) if q0.5 Tail (r=0) if q0.5 Any mixed strategy (0?r?1) if q=0.5 Solving matching pennies Player 2’s best responseB2(r): Tail (q=0) if r0.5 Head (q=1) if r0.5 Any mixed strategy (0?q?1) if r=0.5 Solving matching pennies Player 1’s best responseB1(q): Head (r=1) if q0.5 Tail (r=0) if q0.5 Any mixed strategy (0?r?1) if q=0.5 Player 2’s best responseB2(r): Tail (q=0) if r0.5 Head (q=1) if r0.5 Any mixed strategy (0?q?1) if r=0.5 Check r = 0.5 is best response to q=0.5q = 0.5 is best response to r=0.5 Mixed strategy Mixed Strategy: A mixed strategy of a player is a probability distribution over player’s (pure) strategies. Mixed strategy: example Matching pennies Playe