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A Discounted Stochastic Game with No Stationary Nash Equilibrium

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  • Yehuda (John) Levy

Abstract

We present an example of a discounted stochastic game with a continuum of states, finitely many players and actions, and deterministic transitions, that possesses no measurable stationary equilibria, or even stationary approximate equilibria. The example is robust to perturbations of the payoffs, the transitions, and the discount factor, and hence gives a strong nonexistence result for stationary equilibria. The example is a game of perfect information, and hence it also does not possess stationary extensive-form correlated equilibrium. Markovian equilibria are also shown not to exist in appropriate perturbations of our example.

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp596r.

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Length: 25 pages
Date of creation: 11 Jan 2012
Date of revision: May 2012
Handle: RePEc:huj:dispap:dp596r

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Keywords: Stochastic Game; Discounting; Stationary Equilibrium;

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References

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  1. Monahan George E. & Sobel Matthew J., 1994. "Stochastic Dynamic Market Share Attraction Games," Games and Economic Behavior, Elsevier, vol. 6(1), pages 130-149, January.
  2. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
  3. Eric Maskin & Jean Tirole, 1997. "Markov Perfect Equilibrium, I: Observable Actions," Harvard Institute of Economic Research Working Papers 1799, Harvard - Institute of Economic Research.
  4. Harris, Christopher & Reny, Philip & Robson, Arthur, 1995. "The Existence of Subgame-Perfect Equilibrium in Continuous Games with Almost Perfect Information: A Case for Public Randomization," Econometrica, Econometric Society, vol. 63(3), pages 507-44, May.
  5. Amir, Rabah, 1996. "Continuous Stochastic Games of Capital Accumulation with Convex Transitions," Games and Economic Behavior, Elsevier, vol. 15(2), pages 111-131, August.
  6. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
  7. F. Forges, 2010. "An Approach to Communication Equilibrium," Levine's Working Paper Archive 516, David K. Levine.
  8. Chakrabarti, Subir K., 1999. "Markov Equilibria in Discounted Stochastic Games," Journal of Economic Theory, Elsevier, vol. 85(2), pages 294-327, April.
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Citations

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Cited by:
  1. Ziv Hellman, 2012. "A Game with No Bayesian Approximate Equilibria," Discussion Paper Series dp615, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Equilibria: The Case of Absolutely Continuous Transitions," Discussion Paper Series dp612, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  3. Yehuda Levy, 2013. "Continuous-Time Stochastic Games of Fixed Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 279-312, June.
  4. He, Wei & Sun, Yeneng, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," MPRA Paper 51274, University Library of Munich, Germany.
  5. Wei He & Yeneng Sun, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," Papers 1311.1562, arXiv.org.
  6. Jean Guillaume Forand & John Duggan, 2013. "Markovian Elections," Working Papers 1305, University of Waterloo, Department of Economics, revised Oct 2013.

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