The concept of Nash equilibrium has become central in economics. Researchers in fields such as industrial organization, international economics, economics of information, labor economics and bargaining theory have adopted it as the main theoretical tool for the analysis of interactive strategic behavior. Yet the assumption that agents will play according to Nash equilibrium is questionable because it relies on strong assumptions regarding common knowledge and full rationality of all agents. The goal of this research is to determine under what conditions profit maximizing agents learn to play according to a strategic Nash equilibrium and what are the possible patterns of the limit behaviors when they do not converge to a Nash equilibrium. This is an important line of research because the experimental literature has shown that agents in repeated interactive situations do learn to play Nash equilibrium, but no theoretical explanation for this phenomenon has yet been provided. The research in this project concentrates on rational learning in long term interactions. By rational learning it is meant that players choose actions that optimize their overall payoffs, present and future, with learning being included as part of the overall optimization problem. However, unlike classical game theory, rationality will include no assumption about common knowledge of parameters of the game or strategies of the opponents. The project extends a pathbreaking proof by the investigators that rational learning in two-person games leads to Nash equilibrium if there is a "grain of truth" in the beliefs of the players about each other's likely strategies. These results are extended to games with many players, games with imperfect observability, and to stochastically changing environments. The results will also be studied when players are not completely rational but use finite automata.
