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Quitting Games

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  • Eilon Solan
  • Nicolas Vieille

Abstract

Quitting games are sequential games in which, at any stage, each player has the choice between continuing and quitting. The game ends as soon as at least player chooses to quit; player i then receives a payoff r, which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is 0. We prove the existence of cyclic E-equilibrium under some assumptions on the payoff function (r sub s). We prove on an example that our result is essentially optimal. We also discuss the relation to Dynkin's stopping games, and provide a generalization of our result to these games.

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File URL: http://www.kellogg.northwestern.edu/research/math/papers/1227.pdf
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Bibliographic Info

Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1227.

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Date of creation: Sep 1998
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Handle: RePEc:nwu:cmsems:1227

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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Phone: 847/491-3527
Fax: 847/491-2530
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Web page: http://www.kellogg.northwestern.edu/research/math/
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References

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  1. Wilson, Robert, 1992. "Strategic models of entry deterrence," 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 10, pages 305-329 Elsevier.
  2. Janos Flesch & Frank Thuijsman & Koos Vrieze, 1997. "Cyclic Markov Equilibria in Stochastic Games," International Journal of Game Theory, Springer, vol. 26(3), pages 303-314.
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Citations

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Cited by:
  1. Schweinzer, Paul, 2006. "Sequential bargaining with pure common values," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 137, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  2. Eilon Solan & Nicolas Vieille, 2002. "Stopping games: recent results," Working Papers hal-00242994, HAL.
  3. Eilon Solan, 2000. "The Dynamics of the Nash Equilibrium Correspondence and n-Player Stochastic Games," Discussion Papers 1311, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Michael Ludkovski, 2010. "Stochastic Switching Games and Duopolistic Competition in Emissions Markets," Papers 1001.3455, arXiv.org, revised Aug 2010.
  5. Eilon Solan & Nicolas Vieille, 1998. "Correlated Equilibrium in Stochastic Games," Discussion Papers 1226, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
  7. Schweinzer, Paul, 2006. "Sequential bargaining with pure common values and incomplete information on both sides," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 136, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  8. Nicolas Vieille, 2002. "Stochastic Games : recent results," Working Papers hal-00242996, HAL.
  9. VIEILLE, Nicolas, 2001. "Stochastic games : recent results," Les Cahiers de Recherche 743, HEC Paris.
  10. Eilon Solan, 2002. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Discussion Papers 1356, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  11. Eilon Solan & Rakesh V. Vohra, 1999. "Correlated Equilibrium, Public Signaling and Absorbing Games," Discussion Papers 1272, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Paul Schweinzer, 2003. "Dissolving a Common Value Partnership in a Repeated 'queto' Game," Discussion Paper Series dp318, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  14. Eilon Solan & Nicolas Vieille, 2010. "Computing uniformly optimal strategies in two-player stochastic games," Economic Theory, Springer, vol. 42(1), pages 237-253, January.

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