Fuzzily Constrained Games

Youzhi Zhang, Xudong Luo, Ho-fung Leung

Abstract: In real life, games are often played in contexts. So, when a player of a game chooses a strategy, it should consider not only the material or money payoff from taking the strategy and others' best response but also how feasible to take the strategy in the specific context where the game is played. To solve such a game, this paper establishes a model of fuzzily constrained games and introduces a solution concept of constrained equilibrium for the games of this kind. Our model can reflect the outcome of altruistic behavior and predict the outcome of a game played under fuzzy constraints precisely. Finally, we discuss what will happen if Prisoner's Dilemma and Stag Hunt are played under fuzzy constraints.