Language-Based Games

We introduce language-based games, in which utility is defined over descriptions in a given language. By choosing the right language, we can capture psychological games [9] and reference-dependent preference [15]. Of special interest are languages that can express only coarse beliefs (e.g., the probability of an event is "high" or "low", rather than "the probability is .628"): by assuming that a player's preferences depend only on what is true in a coarse language, we can resolve a number of well-known paradoxes in the literature, including the Allais paradox. Despite the expressive power of this 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 on the language