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Stochastic Nash Equilibrium Seeking for Games with General Nonlinear Payoffs

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Stochastic Averaging and Stochastic Extremum Seeking

Part of the book series: Communications and Control Engineering ((CCE))

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Abstract

Extremum seeking is extended from standard multi-input optimization problems to multi-player non-cooperative games. The players do not have knowledge of the payoff functions and only measure their own payoff values. The players are also unaware of the other players’ actions. Extremum seeking is shown to achieve convergence to the Nash equilibrium of the underlying static game.

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References

  1. Altman E, Başar T, Srikant R (2002) Nash equilibria for combined flow control and routing in networks: asymptotic behavior for a large number of users. IEEE Trans Autom Control 47:917–930

    Article  Google Scholar 

  2. Başar T (2007) Control and game-theoretic tools for communication networks (overview). Appl Comput Math 6:104–125

    MathSciNet  MATH  Google Scholar 

  3. Başar T, Olsder GJ (1999) Dynamic noncooperative game theory, 2nd edn. SIAM, Philadelphia

    MATH  Google Scholar 

  4. Bauso D, Giarre L, Pesenti R (2008) Consensus in noncooperative dynamic games: a multiretailer inventory application. IEEE Trans Autom Control 53:998–1003

    Article  MathSciNet  Google Scholar 

  5. Cesa-Bianchi N, Lugosi G (2006) Prediction, learning, and games. Cambridge University Press, New York

    Book  MATH  Google Scholar 

  6. Foster DP, Young HP (2003) Learning, hypothesis testing, and Nash equilibrium. Games Econ Behav 45:73–96

    Article  MathSciNet  MATH  Google Scholar 

  7. Foster DP, Young HP (2006) Regret testing: learning to play Nash equilibrium without knowing you have an opponent. Theor Econ 1:341–367

    Google Scholar 

  8. Frihauf P, Krstic M, Başar T (2012) Nash equilibrium seeking in noncooperative games. IEEE Trans Autom Control 57:1192–1207

    Article  Google Scholar 

  9. Fudenberg D, Levine DK (1998) The theory of learning in games. MIT Press, Cambridge

    MATH  Google Scholar 

  10. Jafari A, Greenwald A, Gondek D, Ercal G (2001) On no-regret learning, fictitious play, and Nash equilibrium. In: Proceedings of the 18th international conference on machine learning

    Google Scholar 

  11. Krstic M, Frihauf P, Krieger J, Başar T (2010) Nash eqilibrium seeking with finitely- and infinitely-many players. In: Proceedings of the 8th IFAC symposium on nonlinear control systems, Bologna, Italy

    Google Scholar 

  12. Kubica BJ, Wozniak A (2010) An interval method for seeking the Nash equilibrium of non-cooperative games. In: Parallel processing and applied mathematics. Lecture notes in computer science, vol. 6068. Springer, Berlin, pp 446–455

    Chapter  Google Scholar 

  13. Li S, Başar T (1987) Distributed algorithms for the computation of noncooperative equilibria. Automatica 23:523–533

    Article  MATH  Google Scholar 

  14. Liu S-J, Krstic M (2010) Stochastic averaging in continuous time and its applications to extremum seeking. IEEE Trans Autom Control 55(10):2235–2250

    Article  MathSciNet  Google Scholar 

  15. Liu S-J, Krstic M (2011) Stochastic Nash equilibrium seeking for games with general nonlinear payoffs. SIAM J Control Optim 49:1659–1679

    Article  MathSciNet  MATH  Google Scholar 

  16. MacKenzie AB, Wicker SB (2001) Game theory and the design of self-configuring, adaptive wireless networks. IEEE Commun Mag 39:126–131

    Article  Google Scholar 

  17. Marden JR, Arslon G, Shamma JS (2009) Cooperative control and potential games. IEEE Trans Syst Man Cybern, Part B, Cybern 39:1393–1407

    Article  Google Scholar 

  18. Rao SS, Venkayya VB, Khot NS (1988) Game theory approach for the integrated design of structures and controls. AIAA J 26:463–469

    Article  MathSciNet  MATH  Google Scholar 

  19. Rosen JB (1965) Existence and uniqueness of equilibrium points for concave N-person games. Econometrica 33:520–534

    Article  MathSciNet  MATH  Google Scholar 

  20. Scutari G, Palomar DP, Barbarossa S (2009) The MIMO iterative waterfilling algorithm. IEEE Trans Signal Process 57:1917–1935

    Article  Google Scholar 

  21. Semsar-Kazerooni E, Khorasani K (2009) Multi-agent team cooperation: a game theory approach. Automatica 45:2205–2213

    Article  MathSciNet  MATH  Google Scholar 

  22. Shamma JS, Arslan G (2005) Dynamic fictitious play, dynamic gradient play, and distributed convergence to Nash equilibria. IEEE Trans Autom Control 53(3):312–327

    Article  MathSciNet  Google Scholar 

  23. Sharma R, Gopal M (2010) Synergizing reinforcement learning and game theory—a new direction for control. Appl Soft Comput 10(3):675–688

    Article  Google Scholar 

  24. Stanković MS, Johansson KH, Stipanović DM (2010) Distributed seeking of Nash equilibrium in mobile sensor networks. In: Proceedings of IEEE conference on decision and control, Atlanta, GA, USA, December 15–17, pp 5598–5603

    Google Scholar 

  25. Tan Y, Nešić D, Mareels IMY (2006) On non-local stability properties of extremum seeking controllers. Automatica 42:889–903

    Article  MATH  Google Scholar 

  26. Zhu M, Martinez S (2010) Distributed coverage games for mobile visual sensor networks. SIAM J Control Optim (submitted). Available at http://arxiv.org/abs/1002.0367

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Authors and Affiliations

  1. Department of Mathematics, Southeast University, Nanjing, People’s Republic of China

    Shu-Jun Liu

  2. Department Mechanical & Aerospace Engineering, University of California, San Diego, La Jolla, California, USA

    Miroslav Krstic

Authors
  1. Shu-Jun Liu
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  2. Miroslav Krstic
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Correspondence to Miroslav Krstic .

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© 2012 Springer-Verlag London

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Liu, SJ., Krstic, M. (2012). Stochastic Nash Equilibrium Seeking for Games with General Nonlinear Payoffs. In: Stochastic Averaging and Stochastic Extremum Seeking. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-4087-0_9

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  • DOI: https://doi.org/10.1007/978-1-4471-4087-0_9

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-4086-3

  • Online ISBN: 978-1-4471-4087-0

  • eBook Packages: EngineeringEngineering (R0)

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