混合策略Nash均衡的风险特性及其影响研究

Study on Risks of Mixed Strategy Nash Equilibrium and Its Effects

首先指出了当博弈达到混合策略Nash均衡时,对于博弈参与者而言存在着一定的决策风险。但是由于一般决策问题与博弈问题之间存在着显著的差异,所以传统的应用于决策的风险度量方法不能直接应用于博弈决策的风险度量。于是笔者结合博弈决策问题的特点,给出了一种结合博弈参与者的期望效用、策略的不确定性以及绝对风险厌恶系数的风险度量方法。并在该风险度量的基础上,讨论了参与者的风险类型对于博弈均衡实现的影响。

In this paper, the authors first point out that game players are faced with some risk of decision-making when mixed strategy Nash equilibrium is achieved, and that the risk can not be directly measured with the conventional methods applied in weighing risks of general decision-making because this is the case with a game. Therefore, by integrating the expected utility, uncertainty and the absolute risk aversion coefficient of players, the authors present a new method to measure the risk facing the players in a game, on the basis of which the authors discuss the effects on the realization of equilibrium in game playing.