Correlated Equilibria and Mean Field Games: A Simple Model

Luciano Campi () and Markus Fischer ()
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Luciano Campi: Department of Mathematics “Federigo Enriques,” University of Milan, 20133 Milan, Italy
Markus Fischer: Department of Mathematics “Tullio Levi-Civita,” University of Padua, 35121 Padova, Italy

Mathematics of Operations Research, 2022, vol. 47, issue 3, 2240-2259

Abstract: In the context of simple finite-state discrete time systems, we introduce a generalization of a mean field game solution, called a correlated solution, which can be seen as the mean field game analogue of a correlated equilibrium . Our notion of a 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.

Keywords: Primary: 91A15; 91B70; secondary: 93E20; Nash equilibrium; correlated equilibrium; mean field game; weak convergence; restricted strategy; exchangeability (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:3:p:2240-2259

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