Seminar Event Detail


Financial/Actuarial Mathematics

Date:  Wednesday, November 18, 2015
Location:  1360 East Hall (4:00 PM to 5:00 PM)

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 rational agents, 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 payed 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.

Files: 3251_UMich-MFG.pdf


Speaker:  Daniel Lacker
Institution:  Brown University

Event Organizer:   Erhan Bayraktar    erhan@umich.edu

 

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