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Robust Mean Field Games

Author

Listed:
  • Dario Bauso

    (Università di Palermo)

  • Hamidou Tembine

    (Ecole Supérieure d’Electricité, Supelec)

  • Tamer Başar

    (University of Illinois at Urbana-Champaign)

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.

Suggested Citation

  • Dario Bauso & Hamidou Tembine & Tamer Başar, 2016. "Robust Mean Field Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 277-303, September.
    • Handle: RePEc:spr:dyngam:v:6:y:2016:i:3:d:10.1007_s13235-015-0160-4
    DOI: 10.1007/s13235-015-0160-4
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    1. Sergiu Hart, 2013. "Adaptive Heuristics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 11, pages 253-287, World Scientific Publishing Co. Pte. Ltd..
    2. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 691-705, August.
    3. Sergiu Hart & Andreu Mas-Colell, 2013. "A General Class Of Adaptive Strategies," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 3, pages 47-76, World Scientific Publishing Co. Pte. Ltd..
    4. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    5. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-228, February.
    6. Xavier Spinat, 2002. "A Necessary and Sufficient Condition for Approachability," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 31-44, February.
    7. Sergiu Hart & Andreu Mas-Colell, 2013. "Regret-Based Continuous-Time Dynamics," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 5, pages 99-124, World Scientific Publishing Co. Pte. Ltd..
    8. Foster, Dean P. & Vohra, Rakesh, 1999. "Regret in the On-Line Decision Problem," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 7-35, October.
    9. Lehrer, Ehud, 2003. "A wide range no-regret theorem," Games and Economic Behavior, Elsevier, vol. 42(1), pages 101-115, January.
    10. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(5), pages 879-883, October.
    11. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(2), pages 411-413, April.
    12. Ehud Lehrer & Eilon Solan, 2006. "Excludability and Bounded Computational Capacity," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 637-648, August.
    13. Hamidou Tembine & Quanyan Zhu & Tamer Basar, 2011. "Risk-sensitive mean field stochastic differential games," Post-Print hal-00643547, HAL.
    14. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    15. ,, 2003. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 19(6), pages 1195-1198, December.
    16. Dario Bauso & Ehud Lehrer & Eilon Solan & Xavier Venel, 2015. "Attainability in Repeated Games with Vector Payoffs," Mathematics of Operations Research, INFORMS, vol. 40(3), pages 739-755, March.
    17. Nicolas Vieille, 1992. "Weak Approachability," Post-Print hal-00481891, HAL.
    18. Lehrer, Ehud & Solan, Eilon, 2009. "Approachability with bounded memory," Games and Economic Behavior, Elsevier, vol. 66(2), pages 995-1004, July.
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    Cited by:

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