对粗糙集上的不完全信息非合作博弈的均衡分析

Equilibrium Analysis of Non-Cooperative Game with Incomplete Information on Rough Set

在经典不完全信息非合作博弈中,常常假定局中人知道其他局中人类型的概率分布,但是在现实的社会中,对于这样的概率分布往往无法知晓.本文借助粗糙集理论处理这种不完备性,首先利用其中一个局中人依赖于对其他局中人的信息判断,计算出其他局中人的类型近似精确度.其次,给出模型的Nash均衡的存在性定理,并利用Kakutani-Fan-Glicksberg不动点定理证明了Nash均衡的存在性.最后,通过一个实例验证了该博弈模型的实用性.

In classical non-cooperative games with incomplete information,it is often assumed that the players know the probability distribution of other players,but in the real society,such probability distribution is often unknown.In this paper,rough set theory is used to deal with this incompleteness,and the type approximation accuracy of other players is calculated by using the information judgment of one player on other players.Secondly,the existence theorem of Nash equilibrium is given,and the existence of Nash equilibrium is proved by Kakutani-Fan-Glicksberg fixed point theorem.Finally,an example is given to verify the practicability of the game model.