Fuzzy contributive games: an extension to the game of civic duty

Abstract

Game theory deals with decision-making processes involving two or more parties with partly or completely conflicting interests. The players involved in the game usually make their decisions under conditions of risk or uncertainty. In this paper, an idea of nondeterministic payoffs is proposed and optimization is done in a more realistic fuzzy environment, helping each player describe his goal functions by using the linguistic variables. Since fuzzy numbers represent uncertain numeric values, their substitution for traditional crisp payoff values is described and their application is surveyed for a specific sample of contributive games - the game of civic duty. A closed formulation is developed for a vast general class of vague payoffs