Games Played under Fuzzy Constraints

Psychological experiment studies reveal that human interaction behaviors are often not the same as what game theory predicts. One of important reasons is that they did not put relevant constraints into consideration when the players choose their best strategies. However, in real life, games are often played in certain contexts where players are constrained by their capabilities, law, culture, custom, and so on. For example, if someone wants to drive a car, he/she has to have a driving license. Therefore, when a human player of a game chooses a strategy, he/she should consider not only the material payoff or monetary reward from taking his/her best strategy and others' best responses but also how feasible to take the strategy in that 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 is consistent with psychological experiment results of ultimatum games. We also discuss what will happen if Prisoner's Dilemma and Stag Hunt are played under fuzzy constraints. In general, after putting constraints into account, our model can reflect well the human behaviors of fairness, altruism, self-interest, and so on, and thus can predict the outcomes of some games more accurate than conventional game theory.