Monday, May 3, 2010
5130 Upson Hall
A range of modern systems, such as markets, transportation systems, and online social systems, are characterized by dynamic interactions among a large population of agents. While game theoretic methods appear to hold promise for providing insight into incentives of agents in such systems, they often struggle in the face of the curse of dimensionality: as the number of agents increases, full subgame perfect equilibrium in such systems relies on increasingly complex state information, and becomes an increasingly implausible as a model of reality.
Instead, we consider an approach recently introduced in a range of applications across economics, operations research, and control theory: mean field equilibrium (MFE). In MFE, each player reacts to only the long run average state of other players. MFE is a valuable modeling tool: rather than facing intractability as the number of agents increases, MFE uses this largesse to its advantage to reduce complexity. This talk focuses on basic questions regarding existence, approximation, and convergence. When does MFE exist? When is it a good approximation to behavior in finite games? And when do natural learning algorithms converge to MFE? We discuss answers to each of these questions for several models of interest, and also survey extensions and future directions.