极大熵准则下n人非合作条件博弈的期望Nash均衡

Nash Equilibrium in Expectation of n-person Non-cooperative Condition Games under Greatest Entropy Criterion

设每个局中人的纯策略空间都是实数集上的Bore l集,在实数集上有m个确定的L ebesgue可测集,并存在从这n个纯策略空间的笛卡尔乘积到实数集的m个n元Bore l函数。这m个Bore l函数在对应L ebesgue可测集下的逆像构成这n个纯策略空间的笛卡尔乘积的一个划分,并且每n-1个纯策略空间的笛卡尔乘积都具有有限正L ebesgue测度。纯策略空间的笛卡尔乘积的不同分块中的纯局势一般具有不同的博弈结果。每个局中人的效用都是自己所选纯策略的一元函数。在极大熵准则是每个局中人的共同知识的条件下,我们得到了求这类博弈的期望意义下的N ash均衡点的方法.给出这种N ash均衡点的存在定理和可交换定理。最后给出一个应用例子。

Let every player＇s pure strategy space be a Borel set on real numbers set R. There are m fixed Lebesgue measurable sets on R, and there are rn Borel functions of n-variables from Cartesian product of n the pure strategy spaces to R. All the inverse image formed by those Borel functions under corresponding Lebesgue measurable sets generate a partition of the Cartesian product. Let Cartesian product of any n-1 spaces of pure strategies have finite positive Lebesgue measure. Pure situations in different blocks of the Cartesian product have different game results, generally. Every player＇s utility is a real function of pure strategy he using. Suppose greatest entropy criterion is every player＇s common knowledge. In this paper, we give a method of finding Nash equilibrium points in expectation. And give existence theorem and commutative theorem of Nash equilibrium points in expectation. Finally, we give an example.