On coset weighted potential game
On coset weighted potential game
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DOI：
10.1016/j.jfranklin.2020.02.040
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发表时间：
2019-02
期刊：
影响因子：
--
通讯作者：
Yuanhua Wang;D. Cheng
中科院分区：
文献类型：
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作者：
Yuanhua Wang;D. Cheng
本文首先定义了一类新的势对策，称之为陪集加权势对策，它是加权势对策的一种推广形式。利用矩阵的半张量积，给出了有限对策是否为陪集加权势对策的代数方法，并得到了计算相应势函数的简单公式.揭示了陪集加权势对策的一些性质。最后，借助于有限对策的向量空间结构，提出了一种新的基于陪集权的正交分解，并给出了相应的子空间的几何和代数表达式.
In this paper we first define a new kind of potential games, called coset weighted potential game, which is a generalized form of weighted potential game. Using semi-tensor product of matrices, an algebraic method is provided to verify whether a finite game is a coset weighted potential game, and a simple formula is obtained to calculate the corresponding potential function. Then some properties of coset weighted potential games are revealed. Finally, by resorting to the vector space structure of finite games, a new orthogonal decomposition based on coset weights is proposed, the corresponding geometric and algebraic expressions of all the subspaces are given by providing their bases.