摘要：AbstractZero-sum game is a class of game where one player’s gain is equivalent to another’s loss, which can be used in competitive situation. But pure Nash equilibrium maybe not exist in general zero-sum games. Potential games have nice properties, such as existence of pure Nash equilibrium. To combine advantages of zero-sum games and potential games, zero-sum potential game is proposed in this paper. Verification for a finite non-cooperative game being a zero-sum potential game is considered. Conversely, how to design a zero-sum potential game is also studied when the potential function is given. We show that verification and design of zero-sum potential game can be realized by solving linear equations. Furthermore, we find that if any two players play the zero-sum potential game in a network, then the networked game is also a zero-sum potential game.
关键词：KeywordsZero-sum gamepotential gamenetworked evolutionary gamesemi-tensor product of matriceslinear equationverificationsdesign
