The general framework is that of game theory, with multiple participants ( players ) that interact repeatedly over time. The players may be people, corporations, nations, computers even genes. While many of the standard concepts of game theory are static by their very nature (for example, strategic equilibria and cooperative solutions), it is of utmost importance theoretically as well as in applications to study dynamic processes, and relate them to appropriate static solutions. This is a fundamental issue. On the one hand, the significance of a solution depends in particular on how easy it is to reach it. On the other hand, natural dynamics, that is, processes that to a certain degree reflect observed behaviors and actual institutions, are important to study and understand in their own right. We propose to work on three main areas. First, adaptive dynamics: the goal is to characterize those classes of dynamics for which convergence to Nash or correlated equilibria can be obtained, and those for which it cannot, and to find and study natural dynamics that are related to actual behavior and yield useful insights. Second, evolutionary dynamics: the goal is to investigate evolutionary and similar dynamics, with a particular emphasis on understanding the role that large populations may play, and on characterizing which equilibria are evolutionarily stable and which are not. Third, bargaining and cooperation: the goal is to develop a general research program that studies natural bargaining procedures that lead to cooperation and are based directly on the strategic form; some particular aims are to establish connections between the bargaining institutions and the resulting cooperative solutions, and to analyze relevant economic models.
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