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Laplace principle for large population games with control interaction

Author

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  • Luo, Peng
  • Tangpi, Ludovic

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 state processes satisfy a Sanov-type large deviation principle. The results require existence of a Lipschitz continuous solution of the master equation of the corresponding mean field game, and they carry over to cooperative (i.e. central planner) games. We study a linear-quadratic case of such games in details.

Suggested Citation

  • Luo, Peng & Tangpi, Ludovic, 2024. "Laplace principle for large population games with control interaction," Stochastic Processes and their Applications, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:spapps:v:171:y:2024:i:c:s0304414924000206
    DOI: 10.1016/j.spa.2024.104314
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