Language-based games

We introduce language-based games, a generalization of psychological games [Geanakoplos et al., 1989] that can also capture reference-dependent preferences [Ko′szegi and Rabin, 2006], which extend the domain of the utility function to situations, maximal consistent sets in some language. The role of the underlying language in this framework is thus particularly critical. Of special interest are languages that can express only coarse beliefs [Mullainathan, 2002]. Despite the expressive power of the approach, we show that it can describe games in a simple, natural way. Nash equilibrium and rationalizability are generalized to this setting; Nash equilibrium is shown not to exist in general, while the existence of rationalizable strategies is proved under mild conditions.