有序势博弈及其在智能体无线网络中的应用

Ordinal potential game and its application in agent wireless networks

有序势博弈具有广泛的应用,势有向图中不含单向圈是判定有序势博弈的一个充分必要条件.利用矩阵半张量积和置换矩阵,通过博弈的支付矩阵求取势有向图的邻接矩阵.通过收缩势有向图中的双向圈,将单向圈的存在性问题转化为判断收缩后的图中圈的存在性问题.此外,分析有序势函数的一些基本性质,并给出有序势函数的具体计算方法.最后结合线性规划讨论了有序势博弈在延长智能体无线网络系统寿命的应用.

The ordinal potential game has a large number of applications.It is proved that a finite game is ordinal potential game if and only if its potential directed graph（PDG） contains no unidirectional circle.The adjacency matrix of PDG is obtained by the payoff matrix.By Reducing connected bidirectional circles into a node, the problem of judging the existence of unidirectional circles is converted, into testifying the existence of cycles in the reduced graph.Furthermore,some properties of ordinal potential function（OPF） and its calculating method are presented.Finally, combined with linear programming, the application of ordinal potential game in prolonging the lifetime of agent wireless networks is studied.