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Zero-sum constrained stochastic games with independent state processes

Author

Listed:
  • Eitan Altman
  • Konstantin Avrachenkov
  • Richard Marquez
  • Gregory Miller

Abstract

We consider a zero-sum stochastic game with side constraints for both players with a special structure. There are two independent controlled Markov chains, one for each player. The transition probabilities of the chain associated with a player as well as the related side constraints depend only on the actions of the corresponding player; the side constraints also depend on the player’s controlled chain. The global cost that player 1 wishes to minimize and that player 2 wishes to maximize, depend however on the actions and Markov chains of both players. We obtain a linear programming formulations that allows to compute the value and saddle point policies for this problem. We illustrate the theoretical results through a zero-sum stochastic game in wireless networks in which each player has power constraints Copyright Springer-Verlag 2005

Suggested Citation

  • Eitan Altman & Konstantin Avrachenkov & Richard Marquez & Gregory Miller, 2005. "Zero-sum constrained stochastic games with independent state processes," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 375-386, December.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:3:p:375-386
    DOI: 10.1007/s00186-005-0034-4
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    References listed on IDEAS

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    1. Gomez-Ramirez, E. & Najim, K. & Poznyak, A. S., 2003. "Saddle-point calculation for constrained finite Markov chains," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1833-1853, August.
    2. A. Hordijk & L. C. M. Kallenberg, 1984. "Constrained Undiscounted Stochastic Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 276-289, May.
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    Cited by:

    1. János Flesch & Gijs Schoenmakers & Koos Vrieze, 2009. "Stochastic games on a product state space: the periodic case," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 263-289, June.
    2. Flesch, J. & Schoenmakers, G.M. & Vrieze, K., 2007. "Stochastic games on a product state space," Research Memorandum 010, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    3. Olivier Compte & Andrew Postlewaite, 2007. "Effecting Cooperation," PIER Working Paper Archive 09-019, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 29 May 2009.
    4. Compte, Olivier & Postlewaite, Andrew, 2015. "Plausible cooperation," Games and Economic Behavior, Elsevier, vol. 91(C), pages 45-59.
    5. János Flesch & Gijs Schoenmakers & Koos Vrieze, 2008. "Stochastic Games on a Product State Space," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 403-420, May.
    6. Flesch, J. & Schoenmakers, G.M. & Vrieze, K., 2008. "Stochastic games on a product state space: the periodic case," Research Memorandum 016, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    7. Andrew Postlewaite & Olivier Compte, 2008. "Repeated Relationships with Limits on Information Processing," PIER Working Paper Archive 08-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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