  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.
