Representing Strategic Games and Their Equilibria in Many-Valued Logics
  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. 
Libor B\v{e}hounek, Petr Cintula, Chris Ferm\"uller, Tom\'a\v{s}   Kroupa
math.LO