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Stochastic games: Recent results

In: Handbook of Game Theory with Economic Applications

Listed author(s):
  • Vieille, Nicolas

This chapter presents developments in the theory of stochastic games that have taken place in recent years. It complements the contribution by Mertens. Major emphasis is put on stochastic games with finite state and action sets. In the zero-sum case, a classical result of Mertens and Neyman states that given [epsilon] > 0, each player has a strategy that is [epsilon]-optimal for all discount factors close to zero. Extensions to non-zero-sum games are dealt with here. In particular, the proof of existence of uniform equilibrium payoffs for two-player games is discussed, as well as the results available for more-than-two-player games. Important open problems related to N-player games are introduced by means of a class of simple stochastic games, called quitting, or stopping, games. Finally, recent results on zero-sum games with imperfect monitoring and on zero-sum games with incomplete information are surveyed.

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This chapter was published in:
  • R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3, December.
  • This item is provided by Elsevier in its series Handbook of Game Theory with Economic Applications with number 3-48.
    Handle: RePEc:eee:gamchp:3-48
    Contact details of provider: Web page: http://www.elsevier.com/wps/find/bookseriesdescription.cws_home/BS_HE/description

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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    1. Zamir, Shmuel, 1992. "Repeated games of incomplete information: Zero-sum," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 5, pages 109-154 Elsevier.
    2. Sorin, Sylvain, 1992. "Repeated games with complete information," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 4, pages 71-107 Elsevier.
    3. Nicolas Vieille & Eilon Solan, 2001. "Quitting Games," Post-Print hal-00465043, HAL.
      • Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    4. repec:dau:papers:123456789/6231 is not listed on IDEAS
    5. MERTENS, Jean-François, "undated". "Stochastic games," CORE Discussion Papers RP 1587, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Donald A. Walker (ed.), 2000. "Equilibrium," Books, Edward Elgar Publishing, volume 0, number 1585.
    7. Eilon Solan & Nicolas Vieille, 2002. "Correlated Equilibrium in Stochastic Games," Post-Print hal-00465020, HAL.
    8. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, October.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, October.
    9. Aumann, Robert J. & Heifetz, Aviad, 2001. "Incomplete Information," Working Papers 1124, California Institute of Technology, Division of the Humanities and Social Sciences.
    10. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476.
    11. Frank Thuijsman & Thirukkannamangai E. S. Raghavan, 1997. "Perfect Information Stochastic Games and Related Classes," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 403-408.
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