Linguistic Fuzzy-Logic 2x2 Games

Abstract

AbstractConventional game theory faces a dilemma rooted in an incompatibility between the Boolean-logical foundation of the logic of the game and the linguistic nature of strategic communication – linguistic fuzzy logic which ”computes with words” all the way down offers a way out of this dilemma. On the one hand, gametheoretic methodologies are inescapably based on a posited underlying logic. The latter is what guides us in judging whether a game-theoretic methodology (and theory) possesses logical coherence and consistency. Boolean two-valued logic underpins conventional game theory. All game-theoretic arguments and the very notion of consistency and inconsistency are based on a sharp Boolean-logic true/false dichotomy. On the other hand, vagueness and equivocation are constitutive features of human communication. Human beings cannot live and communicate without a ”language,” with the latter being inherently vague. Game theory is essentially the study of strategic communication of information through language in a rigorous and stylized way. However, stylization and rigor cannot totally eradicate vagueness – there is always a remainder of linguistic vagueness at the very heart of the conceptual tools – communicative devices – used in game theory. This creates a foundational dilemma for conventional game theory. Is it possible to resolve this incompatibility between, on the one hand, taking the dichotomous Boolean two-valued logic as the logical foundation of game theory and, on the other hand, the vagueness that inheres in strategic communication due to the very nature of language? This difficulty is often glossed over or not even sensed at all in conventional game-theoretic works. I propose a remedy to this dilemma by anchoring game theory in linguistic fuzzy logic.KeywordsNash EquilibriumBoolean LogicCheap TalkTrust GameFull CooperationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.