Representing Strategic Games and Their Equilibria in Many-Valued Logics

TL;DR

This paper introduces logical A-games, a general framework for representing strategic games and their Nash equilibria using many-valued logics, extending Boolean and Lukasiewicz games to a broader class of algebras.

Contribution

It generalizes existing game representations to a wide class of many-valued logics and provides methods to construct formulas for Nash equilibria within this framework.

Findings

Logical A-games can represent a broad class of strategic games.

Methods to construct propositional formulas for pure and mixed Nash equilibria.

Extension of Boolean and Lukasiewicz games to general algebras.

Abstract

We introduce the notion of logical A-games for a fairly general class of algebras A of real truth-values. This concept generalizes the Boolean games of Harrenstein et al. as well as the recently defined Lukasiewicz games of Marchioni and Wooldridge. We demonstrate that a wide range of strategic n-player games can be represented as logical A-games. Moreover we show how to construct, under rather general conditions, propositional formulas in the language of A that correspond to pure and mixed Nash equilibria of logical A-games.