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Recursive Methods in Discounted Stochastic Games: An Algorithm for delta Approaching 1 and a Folk Theorem

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Abstract

We present an algorithm to compute the set of perfect public equilibrium payoffs as the discount factor tends to one for stochastic games with observable states and public (but not necessarily perfect) monitoring when the limiting set of (long-run players') equilibrium payoffs is independent of the state. This is the case, for instance, if the Markov chain induced by any Markov strategy profile is irreducible. We then provide conditions under which a folk theorem obtains: if in each state the joint distribution over the public signal and next period’s state satisfies some rank condition, every feasible payoff vector above the minmax payoff is sustained by a perfect public equilibrium with low discounting.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1742.

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Length: 46 pages
Date of creation: Dec 2009
Date of revision: Aug 2010
Publication status: Published in Econometrics (July 2011), 79(4): 1277-1318
Handle: RePEc:cwl:cwldpp:1742

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Keywords: Stochastic games;

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  1. Roger Lagunoff & Akihiko Matsui, 1997. "Asynchronous Choice in Repeated Coordination Games," Game Theory and Information 9707002, EconWPA.
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  7. Phelan, Christopher, 2006. "Public trust and government betrayal," Journal of Economic Theory, Elsevier, vol. 130(1), pages 27-43, September.
  8. Yoon, Kiho, 2001. "A Folk Theorem for Asynchronously Repeated Games," Econometrica, Econometric Society, vol. 69(1), pages 191-200, January.
  9. Rotemberg, Julio J & Saloner, Garth, 1986. "A Supergame-Theoretic Model of Price Wars during Booms," American Economic Review, American Economic Association, vol. 76(3), pages 390-407, June.
  10. Maskin, Eric & Kreps, David & Fudenberg, Drew, 1990. "Repeated Games with Long-run and Short-run Players," Scholarly Articles 3226950, Harvard University Department of Economics.
  11. A. J. Hoffman & R. M. Karp, 1966. "On Nonterminating Stochastic Games," Management Science, INFORMS, vol. 12(5), pages 359-370, January.
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  13. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832 Elsevier.
  14. Mertens, J.-F. & Parthasarathy, T., 1987. "Equilibria for discounted stochastic games," CORE Discussion Papers 1987050, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  15. Radner, Roy & Myerson, Roger & Maskin, Eric, 1986. "An Example of a Repeated Partnership Game with Discounting and with Uniformly Inefficient Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 59-69, January.
  16. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series dp295, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  17. Christopher Phelan, 2001. "Public trust and government betrayal," Staff Report 283, Federal Reserve Bank of Minneapolis.
  18. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 53-82, January.
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