Abstract

We introduce language-based games, a generalization of psychological games [Geanakoplos, Pearce, and Stacchetti, 1989] that can also capture reference-dependent preferences [Koszegi 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 thus becomes particularly critical. Of particular interest are situations where the language can express only coarse beliefs [Mullainathan, 2002]. Despite the expressive power of the approach, we show that it 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.

Language-Based Games (Extended Abstract) / 2967 Adam Bjorndahl, Joseph Y. Halpern, Rafael Pass We introduce language-based games, a generalization of psychological games [Geanakoplos, Pearce, and Stacchetti, 1989] that can also capture reference-dependent preferences [Koszegi 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 thus becomes particularly critical. Of particular interest are situations where the language can express only coarse beliefs [Mullainathan, 2002]. Despite the expressive power of the approach, we show that it 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.