 Strategic decompositions of normal form games: Zero-sum games and potential gamesSung-Ha Hwang and Luc Rey-Bellet Games and Economic Behavior, 2020, vol. 122, issue C, 370-390 Abstract: We introduce new classes of games, called zero-sum equivalent games and zero-sum equivalent potential games, and prove decomposition theorems involving these classes of games. Two games are “strategically equivalent” if, for every player, the payoff differences between two strategies (holding other players' strategies fixed) are identical. A zero-sum equivalent game is a game that is strategically equivalent to a zero-sum game; a zero-sum equivalent potential game is a potential game that is strategically equivalent to a zero-sum game. We also call a game “normalized” if the sum of one player's payoffs, given the other players' strategies, is zero. One of our main decomposition results shows that any normal form game, whether the strategy set is finite or continuous, can be uniquely decomposed into a zero-sum normalized game, a zero-sum equivalent potential game, and an identical interest normalized game, each with distinctive equilibrium properties. Keywords: Decomposition; Zero-sum games; Potential games (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:gamebe:v:122:y:2020:i:c:p:370-390 DOI: 10.1016/j.geb.2020.05.003 Access Statistics for this article Games and Economic Behavior is currently edited by E. Kalai More articles in Games and Economic Behavior from Elsevier |
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