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Nonzero-sum Stochastic Games

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Author Info

  • Nowak, Andrzej S.
  • Szajowski, Krzysztof

Abstract

This paper treats of stochastic games. We focus on nonzero-sum games and provide a detailed survey of selected recent results. In Section 1, we consider stochastic Markov games. A correlation of strategies of the players, involving ``public signals'', is described, and a correlated equilibrium theorem proved recently by Nowak and Raghavan for discounted stochastic games with general state space is presented. We also report an extension of this result to a class of undiscounted stochastic games, satisfying some uniform ergodicity condition. Stopping games are related to stochastic Markov games. In Section 2, we describe a version of Dynkin's game related to observation of a Markov process with random assignment mechanism of states to the players. Some recent contributions of the second author in this area are reported. The paper also contains a brief overview of the theory of nonzero-sum stochastic games and stopping games which is very far from being complete.

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File URL: http://mpra.ub.uni-muenchen.de/19995/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 19995.

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Date of creation: 1998
Date of revision: 1999
Handle: RePEc:pra:mprapa:19995

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Related research

Keywords: average payoff stochastic games; correlated stationary equilibria; nonzero-sum games; stopping time; stopping games;

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References

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  1. MERTENS, Jean-François & PARTHASARATHY, T., . "Equilibria for discounted stochastic games," CORE Discussion Papers RP -1666, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Dutta, P.K., 1991. "What Do Discounted Optima Converge To? A Theory of Discount Rate Asymptotics in Economic Models," RCER Working Papers 264, University of Rochester - Center for Economic Research (RCER).
  3. Yasuda, M., 1985. "On a randomized strategy in Neveu's stopping problem," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 159-166, December.
  4. Nowak Andrzej S., 1994. "Zero-Sum Average Payoff Stochastic Games with General State Space," Games and Economic Behavior, Elsevier, vol. 7(2), pages 221-232, September.
  5. Forges, Francoise M, 1986. "An Approach to Communication Equilibria," Econometrica, Econometric Society, vol. 54(6), pages 1375-85, November.
  6. Ioannis Karatzas & Martin Shubik & William D. Sudderth, 1992. "Construction of Stationary Markov Equilibria in a Strategic Market Game," Cowles Foundation Discussion Papers 1033, Cowles Foundation for Research in Economics, Yale University.
  7. Vrieze, O J & Thuijsman, F, 1989. "On Equilibria in Repeated Games with Absorbing States," International Journal of Game Theory, Springer, vol. 18(3), pages 293-310.
  8. Christopher Harris, 1991. "The Existence of Subgame-Perfect Equilibrium in Games with Simultaneous Moves," Working papers 570, Massachusetts Institute of Technology (MIT), Department of Economics.
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Citations

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Cited by:
  1. P. Herings & Ronald Peeters, 2010. "Homotopy methods to compute equilibria in game theory," Economic Theory, Springer, vol. 42(1), pages 119-156, January.
  2. Page, F.H., 1994. "Optimal Auction Design with Risk Aversion and Correlated Information," Discussion Paper 1994-109, Tilburg University, Center for Economic Research.
  3. Mabel M. TIDBALL & Eitan ALTMAN, 1994. "Approximations In Dynamic Zero-Sum Games," Game Theory and Information 9401001, EconWPA.
  4. Łukasz Balbus & Kevin Reffett & Łukasz Woźny, 2013. "Markov Stationary Equilibria in Stochastic Supermodular Games with Imperfect Private and Public Information," Dynamic Games and Applications, Springer, vol. 3(2), pages 187-206, June.
  5. Anna Jaśkiewicz & Andrzej Nowak, 2011. "Stochastic Games with Unbounded Payoffs: Applications to Robust Control in Economics," Dynamic Games and Applications, Springer, vol. 1(2), pages 253-279, June.
  6. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Nash Equilibrium," Discussion Paper Series dp596r, The Center for the Study of Rationality, Hebrew University, Jerusalem, revised May 2012.
  7. Shmaya, Eran & Solan, Eilon, 2004. "Zero-sum dynamic games and a stochastic variation of Ramsey's theorem," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 319-329, August.
  8. Eilon Solan & Nicolas Vieille, 2000. "Uniform Value in Recursive Games," Discussion Papers 1293, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  9. Anna Krasnosielska-Kobos & Elżbieta Ferenstein, 2013. "Construction of Nash Equilibrium in a Game Version of Elfving’s Multiple Stopping Problem," Dynamic Games and Applications, Springer, vol. 3(2), pages 220-235, June.
  10. Janusz Matkowski & Andrzej Nowak, 2011. "On discounted dynamic programming with unbounded returns," Economic Theory, Springer, vol. 46(3), pages 455-474, April.
  11. Elżbieta Ferenstein, 2007. "Randomized stopping games and Markov market games," Computational Statistics, Springer, vol. 66(3), pages 531-544, December.
  12. Yuri Kifer, 2012. "Dynkin Games and Israeli Options," Papers 1209.1791, arXiv.org.

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