Mean field limits for stochastic differential games by Daniel Lacker

Event Date: 

Wednesday, December 9, 2015 - 3:30pm to 5:00pm

Event Date Details: 

Refreshments served at 3:15 p.m

Event Location: 

  • South Hall 5607F

Daniel Lacker — Brown University 

Title: Mean field limits for stochastic differential games 

Abstract: Mean field game (MFG) theory generalizes classical models of interacting particle systems by replacing the particles with decision-makers, making the theory applicable in economics and other social sciences. Most research so far has focused on the existence and uniqueness of Nash equilibria in a model which arises intuitively as a continuum limit (i.e., an infinite-agent version) of a given large-population stochastic differential game of a certain symmetric type. This talk discusses some recent results in this direction, particularly for MFGs with common noise, but more attention is paid to recent progress on a less well-understood problem: Given for each n a Nash equilibrium for the n-player game, in what sense if any do these equilibria converge as n tends to infinity? The answer is somewhat unexpected, and certain forms of randomness can prevail in the limit which are well beyond the scope of the usual notion of MFG solution. A new notion of weak MFG solutions is shown to precisely characterize the set of possible limits of approximate Nash equilibria of n-player games, for a large class of models.