Mean Field Equilibrium for Large Scale Stochastic Games

** ****Monday, ****May 3, 2010
4:00pm **

5130 Upson Hall

**Abstract: **

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.