一种求解两两合作轮流博弈问题的混合分裂算法  

A hybrid splitting method for a class of two-by-two alternative games

作　　者：邬烨磊 肖文君 杨亚莉[3] WU Yelei;XIAO Wenjun;YANG Yali(School of Information Science and Technology,ShanghaiTech University,Shanghai 201210,China;College of Sciences,Shanghai University,Shanghai 200444,China;Shanghai Vocational College of Science and Technology,Shanghai 201800 China)

机构地区：[1]上海科技大学信息科学与技术学院 [2]上海大学理学院 [3]上海科学技术职业学院

出　　处：《应用数学与计算数学学报》2018年第2期409-424,共16页Communication on Applied Mathematics and Computation

基　　金：上海市自然科学基金资助项目(09ZR1411100);上海市重点学科建设资助项目(S30104)

摘　　要：提出了一种求解两两合作轮流博弈的四人博弈问题的混合分裂算法.为了模拟实际博弈过程,该算法由两个组内平行分裂算法和一个组间交替极小化算法构成.算法允许对博弈子问题非精确求解,反映了实际博弈中参与人的有限理性,即允许参与人在博弈过程中出现满足一定条件的误差.在适当条件下,证明了所提出的混合分裂算法全局地收敛到所考虑博弈的Nash平衡.A hybrid splitting method is proposed for solving a class of two-by-two alternative games in this paper. To simulate the process of the described game,the proposed method consists of two parts： one is a parallel splitting algorithm between the partners in one group; the other is an alternating minimization method between the two groups. The method allows solving inexactly the sub-problems of the sub-games, and to do so, it matches the bounded rationality of the players in the described game. That is, the players may make some errors which satisfy a certain condition in the game process. The convergence to Nash equilibrium of the proposed method is proved under some suitable conditions.

关 键 词：博弈论 NASH平衡 平行分裂算法 交替极小化算法 

分 类 号：O221.2[理学—运筹学与控制论]