On equivalence of state-based potential games  

作　　者：Han WU Jinhuan WANG 

机构地区：[1]Institute of Mathematics,School of Science,Hebei University of Technology,Tianjin 300401,China

出　　处：《Science China(Information Sciences)》2024年第6期309-323,共15页中国科学（信息科学）（英文版）

基　　金：supported by Natural Science Foundation of Hebei Province(Grant No.F2021202032);Graduate Innovation Funding Program of Hebei Province(Grant No.CXZZSS2023033)。

摘　　要：In this paper,we explore state-based potential games using the semi-tensor product of matrices.First,applying the potential equation,we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game.Next,we present two static equivalence conditions of state-based potential games.We then delve into dynamic equivalence.We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties.Ultimately,we introduce the concept of state-based networked evolutionary games.We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.

关 键 词：semi-tensor product of matrices state-based potential game VERIFICATION EQUIVALENCE state-based networked evolutionary game 

分 类 号：O225[理学—运筹学与控制论]