Linguistic Fuzzy-Logic Social Game of Cooperation

Abstract

I develop a new game-theoretic approach based, not on conventional Boolean two-valued logic, but instead on linguistic fuzzy logic which admits linguistic truth values. A linguistic fuzzy game is defined with linguistic fuzzy strategies, linguistic fuzzy preferences, and the rules of reasoning and inferences of the game operate according to linguistic fuzzy logic, not Boolean logic. This leads to the introduction of a new notion of fuzzy domination and Nash equilibrium which is based not on the usual ‘greater than’ relation ordering but rather on a more general form of relation termed linguistic fuzzy relation. Each agent models others as linguistic fuzzy rational agents and tries to find a linguistic fuzzy Nash equilibrium that will achieve the highest linguistic fuzzy payoff. If the linguistic fuzzy relation is simplified into a crisp two-valued logic, the linguistic fuzzy game reduces to the conventional game. In this article I apply the new approach to situations of non-cooperative twoplayer games such as a 2 × 2 prisoner's dilemma (PD) game and a social game of cooperation with N players. I find that there is always an optimum strong Nash equilibrium which is Pareto optimal, thereby lifting many of the dilemmas that emerge in crisp game theory in two-player and social games.