Strategic decompositions of normal form games: Zero-sum games and potential games

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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.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2020-07
Language
English
Article Type
Article
Citation

GAMES AND ECONOMIC BEHAVIOR, v.122, pp.370 - 390

ISSN
0899-8256
DOI
10.1016/j.geb.2020.05.003
URI
http://hdl.handle.net/10203/275492
Appears in Collection
MT-Journal Papers(저널논문)
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