We study the asymptotic organization among many optimizing individu- als interacting in a suitable “moderate” way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player games. This proof depends upon the derivation of a law of large numbers for the empirical processes in the limit as the number of players tends to infinity. Because it is of independent interest, we prove this result in full detail. We characterize the solutions of the limiting game via a verification argument.

N-PLAYER GAMES AND MEAN FIELD GAMES OF MODERATE INTERACTIONS

Franco Flandoli;Maddalena Ghio;Giulia Livieri
2022

Abstract

We study the asymptotic organization among many optimizing individu- als interacting in a suitable “moderate” way. We justify this limiting game by proving that its solution provides approximate Nash equilibria for large but finite player games. This proof depends upon the derivation of a law of large numbers for the empirical processes in the limit as the number of players tends to infinity. Because it is of independent interest, we prove this result in full detail. We characterize the solutions of the limiting game via a verification argument.
2022
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
interacting populations, moderate interaction, optimal control, mean-field type game.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/111021
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