(eng): 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 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.