求解两人博弈纳什平衡问题的定制临近点算法

Customized proximal point algorithm for Nash equilibrium of two-player games

针对一类不允许校正的两人轮流博弈纳什平衡问题,提出一种定制临近点分裂算法.该算法可用于模拟一种实际博弈活动:参与博弈的两个局中人轮流决策,且在一轮博弈中,每位局中人综合考虑对手上一轮与本轮所给出的决策,根据最优响应规则做出自己的相应决策.在一定假设条件下证明定制临近点算法全局地收敛到所考虑博弈的纳什平衡,数值算例验证了算法的有效性.

For a class of two-player games with alternating offers in which the correction is not permitted, this paper proposes a customized proximal point splitting algorithm. The proposed method could be used to simulate the practical game under considered. In the simulated game, there are two players, and they offer alternatively. At each round of the considered game, each player will take consideration on both of the offers given by his （her） rival at the previous and current round, and then make his （her） own decision based on some optimal response rules. The global convergence to Nash equilibrium of the proposed method is proven under some suitable assumptions. Some preliminary numerical results indicate that the proposed method is valid for the game under consideration.