Robust Mean Field Games

Dario Bauso, Hamidou Tembine, Tamer Başar

Research output: Contribution to journalArticle

Abstract

Recently there has been renewed interest in large-scale games in several research disciplines, with diverse application domains as in the smart grid, cloud computing, financial markets, biochemical reaction networks, transportation science, and molecular biology. Prior works have provided rich mathematical foundations and equilibrium concepts but relatively little in terms of robustness in the presence of uncertainties. In this paper, we study mean field games with uncertainty in both states and payoffs. We consider a population of players with individual states driven by a standard Brownian motion and a disturbance term. The contribution is threefold: First, we establish a mean field system for such robust games. Second, we apply the methodology to production of an exhaustible resource. Third, we show that the dimension of the mean field system can be significantly reduced by considering a functional of the first moment of the mean field process.

Original languageEnglish (US)
Pages (from-to)277-303
Number of pages27
JournalDynamic Games and Applications
Volume6
Issue number3
DOIs
StatePublished - Sep 1 2016

Keywords

  • Differential games
  • Mean field games
  • Optimal control

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

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