应用矩阵半张量积, 博弈论中的一些重要公式可转化为易于计算的矩阵形式. 文章介绍作者近期得到的一些计算公式. 主要包括: 1) 势博弈的检验与势函数的计算; 2) 合作博弈在一致博弈上的展开; 3) Shapley 值的计算. 它们不仅为数值计算提供了有力工具, 同时也为相关的理论研究带来极大的方便.

Using semi-tensor product of matrices, some important formulas in game theory may be converted into their matrix forms, which are easily computable. In this paper some of such formulas obtained by us are introduced. The formulas include mainly the following: 1) The verification for potential game and the calculation of potential functions; 2) the expansion of cooperative games over the set of unanimity games; 3) the calculation of Shapley value of cooperative games. These formulas not only provide convenient tools for numerical calculations, but also become powerful tools for theoreticaresearch.