附关于溷合策略纳什均衡的题解.pdf

关于混合策略的题解 解法之一：PPT 的解法 Mixed Strategies: Matrix Player B L,pL R, 1-pL U,pU (1,2) (0,4) Player A D, 1-pU (0,5) (3,2) For a Nash equilibrium to exist, B must be indifferent between playing Left or Right i.e. 2 + 5(1 - ) = 4 + 2(1 - ) U U U U aU = 3/5 140 Mixed Strategies: Matrix Player B L,pL R, 1-pL 3 U, (1,2) (0,4) 5 Player A 2 D, (0,5) (3,2) 5 For a Nash equilibrium to exist, A must be indifferent between playing Up or Down i.e. = 3(1 ) a = 3/4 L L L 144 1 Only Nash equilibrium: A plays mixed strategy (3/5, 2/5) (from B ) B plays mixed strategy (3/4, 1/4) (from A) 解法之二： 每一方均在对方概率给定 （以及支付组合给定）的条件下，选 择实现自身期望支付最大的概率。 对于player B: 给定π 和支付组合 U ER = π(2 π+ 5(1 π) )+(1- π) (4 π+2(1- π)) B L U U L U U = π(2 π+ 5(1 π) )+ (4 π+2 (1-π)) π(4 π+2(1-π)) L U U U U L U U = π(5-3 π )+ (4 π+2 (1-π)) π(4 π+2(1-π)) L U U U L U U dER B =3-5p = 0 U dp L 3 3 2 p U = A