连续博弈中的混合策略性质及其均衡

在Fudenberg and Tirole（1991，2002）关于纳什均衡的存在性和性质的技术性说明基础上，主要讨论完全信息的连续博弈。对照于刘宗谦（2004，2006）给出的、有限的完全信息静态博弈中的混合策略性质和均衡，它提出并证明连续博弈混合策略集上类似的一些性质，同样利用范一格里克斯伯格不动点定理证明了混合策略纳什均衡的存在性。为强调紧度量空间是可用有限集充分逼近的无限集的数学结构的应用，仿照Myerson（1991，2001）对无限策略集的讨论，它给出了有关的逼近定理的证明，从而也给出了连续博弈混合策略纳什均衡存在性的另一种证明。

The Properties of Mixed Strategies and its Equilibrium in Continuous Game

This paper discusses mainly the continuous game of complete information which is based on the technical explanation about the existence and properties of Nash equilibrium that is has given by Fudenberg and Tirole(1991,2002).In contrast with the properties and equilibrium in mixed strategies in the finite game of static and complete information that is has given by Liu Zongqian(2004),it poses and proves similarly some properties of mixed strategies in the continuous games,and demonstrate alike the existence of Nash equilibrium of mixed strategies using Fan-Glicksberg fixed point theorem.It follows the discussion of infinite strategy space that is has given by Myerson(1991,2001),and proves the approximation theorem that imitates the for stressing the pint that application of mathematical structure of a compact metric space being an infinite set may be approximated by finite ones.Then it proves additionally Nash equilibrium of mixed strategies existence of the continuous games.