Rationality in Games and the Players' Evolving Beliefs
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Abstract
The notion of "rationality" of a player is of central importance in Game Theory and its applications, but its definition is very sensitive to the assumptions we make about the players' beliefs about the game and about each others, as well as about the way these beliefs evolve during the game. The project is to treat these issues in a systematic manner, using a combination of modal logics (a dynamic logic of "actions" for playing the game, and an "epistemic" logic for the players' knowkedge or beliefs), and to investigate the various proposed definitions of "rationality" and their impact on the game's "solution concepts" (i.e. the "best" ways to play the game, e.g. Nash equilibria or backwards induction).
Background Needed
The project assumes some familiarity with basic modal logic or a facility to quickly learn it. In addition, the student will have to learn some basic notions of Game Theory.