Laplace principle for large population games with control interaction
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Publication:6204186
DOI10.1016/J.SPA.2024.104314arXiv2102.04489OpenAlexW4391577734WikidataQ128466170 ScholiaQ128466170MaRDI QIDQ6204186
Author name not available (Why is that?)
Publication date: 27 March 2024
Published in: (Search for Journal in Brave)
Abstract: This work investigates continuous time stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. The control processes are assumed to be open-loop. We give regularity conditions guaranteeing that if the finite-player game admits a Nash equilibrium, then both the sequence of equilibria and the corresponding states processes satisfy a Sanov-type large deviation principle. The result requires existence of a Lipschitz continuous solution of the master equation of the corresponding mean field game, and is based on concentration inequalities for Lipschitz FBSDEs. The result carries over to cooperative (i.e. central planner) games. We study the linear-quadratic case of such games in details.
Full work available at URL: https://arxiv.org/abs/2102.04489
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