Correlated equilibria and mean field games: a simple model

2020/04/13 by Campi, Luciano, Fischer, Markus
#60B10 #91A06 #91A16 #93E20 #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.2004.06185

Abstract

In the context of simple finite-state discrete time systems, we introduce a generalization of mean field game solution, called correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium. Our notion of solution is justified in two ways: We prove that correlated solutions arise as limits of exchangeable correlated equilibria in restricted (Markov open-loop) strategies for the underlying N-player games, and we show how to construct approximate N-player correlated equilibria starting from a correlated solution to the mean field game.

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