一种基于半张量积的多层网络演化博弈方法

Multilayer Evolutionary Networked Games Base on Semi-Tensor Product

针对多层网络演化博弈,采用半张量积方法,遵循短视最优响应策略更新原则,将博弈动态过程进行公式化并研究其策略最优问题。首先,通过半张量积将多层网络演化博弈转化成代数公式的形式,建立相应的转化算法;其次,基于该公式,讨论了博弈的动态行为;最后,通过增加伪玩家到博弈中来研究策略最优问题,目的是设计自由控制序列来最大化伪玩家的平均收益,从而得到最优控制序列。并举例验证了研究结果的有效性。

Using the semi-tensor product method, this paper investigates the algebraic formulation and strategy optimization for a class of multilayer evolutionary networked games with ＂myopic best response adjustment＂ rules. Firstly, the dynamics of the multilayer evolutionary networked game is converted to formulate for the game. Secondly, based on the algebraic form, the dynamic behavior of the multilayer evolutionary networked games is discussed. Finally, the strategy optimization problem is considered by adding a pseudo-player. The aim is to design optimal control sequence to maximize the average income of pseudo-players. An illustrative example shows the effectiveness of this paper.