  We introduce language-based games, a generalization of psychological games
[6] that can also capture reference-dependent preferences [7]. The idea is to
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 [9]. 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.
