Seminar on History and Philosophy of Science
Abstract: We introduce language-based games, based on the thesis that an agent's utility depends on features that are describable in some language. By choosing the right language, we can capture psychological games [Geanakpolos, Pearce, and Stachetti] and reference-dependent preference [Koszegi and Rabin]. 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 an agent's preferences depend only what is true in a coarse language, we show that we can deal in an intuitively satisfactory way with a number of well-known paradoxes in the literature, including the Allais paradox. 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 (that depend on features of the language).
This represents joint work with Adam Bjorndahl and Rafael Pass.