不确定状态下的重复博弈

The Repeated Game Under The Uncertain State

分析非完全信息下个体和群体重复博弈模型.第一阶段,个体和群体之间存在非完全信息博弈;第二阶段,个体根据群体策略比例选择当前情况下的最优策略;第三阶段,部分群体追随者改变自己原来的策略,使得自己策略为当前情况下最优;第四阶段,个体重新选择最优策略,即第二阶段和第三阶段按顺序重复进行.从而得到一个线性二次最优控制问题,并通过相应的Riccati方程得到最优控制问题的一个闭环表示,初步得到标准的线性二次最优控制问题的状态反馈形式进一步解决了线性二次最优控制下的重复博弈问题.

Analyze the repeated game model that individual and group under incomplete information.First stage,exist an incomplete information game between the individual and the group.Second stage,the individual selected the optimal strategy based on the group strategy ratio.Third stage,some followers of group changed their strategy to make their strategy that reached optimal in the current situation.Fourth stage,the individual reselects the optimal strategy.So repeat the second and third stages in sequence.So we got a linear-quadratic optimal control problem.And the closed-loop representation of optimal control problem which are given by Riccati equation.The state feedback form of the linear-quadratic optimal control problem is obtained.Therefore,solved the problem of repeated game which under the linear-quadratic optimal control.