引用本文:徐勇,时胜男,王金环,等.基于群的非完整局势势博弈[J].控制与决策,2020,35(9):2207-2214
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基于群的非完整局势势博弈
徐勇,时胜男,王金环, 苏雪
(河北工业大学理学院,天津300401)
摘要:
针对带有不可行局势的基于群的势博弈,提出基于群的非完整局势势博弈.首先,利用矩阵的半张量积理论,给出判别一个有限博弈是否是基于(强)群的非完整局势势博弈的充分必要条件,即检验一个线性等式是否有解;其次,研究基于群的势博弈与基于群的非完整局势势博弈的关系;最后,给出一个寻找最小不可行局势集的算法,使得有限博弈在剩余局势下是一个基于群的势博弈.
关键词:  势博弈  有限博弈  不可行局势  半张量积  可行集
DOI:10.13195/j.kzyjc.2018.1724
分类号:O225
基金项目:国家自然科学基金项目(71371186).
Group-based potential games with incomplete-profile
XU Yong,SHI Sheng-nan,WANG Jin-huan,SU Xue
(School of Science,Hebei University of Technology,Tianjin300401,China)
Abstract:
In order to investigate the group-based potential games with infeasible profiles, the group-based potential games with incomplete-profile is proposed. Firstly, using the semi-tensor product theory, a method is provided to verify whether a finite game is a (strongly) group-based potential game with incomplete-profile by checking whether a linear equation has a solution. Then, the relationship between the group-based potential games and the group-based potential games with incomplete-profile is studied. Finally, an algorithm is proposed to find the smallest set of infeasible profiles, such that the finite game will be a group-based potential game in the remaining profiles.
Key words:  potential games  finite games  infeasible profiles  semi-tensor product  feasible sets

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