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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.
Ordered potential game has a wide range of applications, the potential digraph does not contain unidirectional loop is to determine the orderly potential game is a necessary and sufficient condition for the use of matrix half-tensor product and displacement matrix, the game through the payment matrix to obtain the potential By contracting the bidirectional loops in the potential digraph, the existence problem of the unidirectional loops is transformed into the existence problem of the circles in the contracted graph.In addition, some basic properties of ordered potential functions , And gives the concrete calculation method of the order potential function.Finally, the application of the orderly potential game to extend the life span of the agent wireless network system is discussed with linear programming.