A Discounted Stochastic Game with No Stationary Nash Equilibrium
AbstractWe 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 InfoPaper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp596r.
Length: 25 pages
Date of creation: 11 Jan 2012
Date of revision: May 2012
Stochastic Game; Discounting; Stationary Equilibrium;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-06-13 (All new papers)
- NEP-GTH-2012-06-13 (Game Theory)
- NEP-HPE-2012-06-13 (History & Philosophy of Economics)
- NEP-MIC-2012-06-13 (Microeconomics)
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- 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.
- Maskin, Eric & Tirole, Jean, 2001.
"Markov Perfect Equilibrium: I. Observable Actions,"
Journal of Economic Theory,
Elsevier, vol. 100(2), pages 191-219, October.
- Eric Maskin & Jean Tirole, 1997. "Markov Perfect Equilibrium, I: Observable Actions," Harvard Institute of Economic Research Working Papers 1799, Harvard - Institute of Economic Research.
- Forges, F., 1984.
"An approach to communication equilibria,"
CORE Discussion Papers
1984035, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
- Chakrabarti, Subir K., 1999. "Markov Equilibria in Discounted Stochastic Games," Journal of Economic Theory, Elsevier, vol. 85(2), pages 294-327, April.
- 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.
- Amir, Rabah, 1996.
"Continuous Stochastic Games of Capital Accumulation with Convex Transitions,"
Games and Economic Behavior,
Elsevier, vol. 15(2), pages 111-131, August.
- AMIR , Rabah, 1995. "Continuous Stochastic Games of Capital Accumulation with Convex Transition," CORE Discussion Papers 1995009, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Ziv Hellman, 2012. "A Game with No Bayesian Approximate Equilibria," Discussion Paper Series dp615, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- He, Wei & Sun, Yeneng, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," MPRA Paper 51274, University Library of Munich, Germany.
- 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.
- Yehuda Levy, 2013.
"Continuous-Time Stochastic Games of Fixed Duration,"
Dynamic Games and Applications,
Springer, vol. 3(2), pages 279-312, June.
- Yehuda (John) Levy, 2012. "Continuous-Time Stochastic Games of Fixed Duration," Discussion Paper Series dp617, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Jean Guillaume Forand & John Duggan, 2013. "Markovian Elections," Working Papers 1305, University of Waterloo, Department of Economics, revised Oct 2013.
- Wei He & Yeneng Sun, 2013. "Stationary Markov Perfect Equilibria in Discounted Stochastic Games," Papers 1311.1562, arXiv.org.
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