The purpose of this project is to examine how the rationality of economic agents and equilibria in games evolve over time through repeated interaction of bounded-rational players. The basic idea is that players do not solve a complicated problem of finding optimal strategies by introspection, but rather they try to solve it by trial and error. Rather than determining players' behavior by an equilibrium, some simple but plausible behavioral assumptions are adopted, and whether the process converges to an equilibrium is examined. The evolution of equilibria in a society where a finite number of players are randomly matched to play a game will be investigated. Relatively unsuccessful strategies are abandoned over time, and occasionally new strategies are introduced by new entrants ("mutations"). While most of the literature on this subject examines the local stability of equilibria with respect to a few one-shot mutations, the long-run, global behavior of the system subject to a series of random mutations will be studied here. A new technique is introduced to analyze the long run distribution of strategies when the mutation rate is vanishingly small, and it is shown that this approach can drastically reduce the set of equilibria. Also, the evolution of pre-play communication will be re-examined in this framework. Game theory has become one of the most fundamental analytical tools in economics and related social sciences. The core of game theoretic analysis is the Nash equilibrium concept. Although widely used, its logical foundations are rather shaky: Namely, we do not have satisfactory answers to the following fundamental questions. How do players come to play a Nash equilibrium, and, if there are many Nash equilibria, which one is chosen? This project will answer those questions in a certain class of situations, where rationality and equilibrium evolve over time through repeated interaction of players.
