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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.

Suggested Citation

  • Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1227
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    References listed on IDEAS

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    1. Janos Flesch & Frank Thuijsman & Koos Vrieze, 1997. "Cyclic Markov Equilibria in Stochastic Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 303-314.
    2. 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.
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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. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
    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. Eilon Solan & Nicolas Vieille, 2001. "Stopping Games: recent results," Working Papers hal-00595484, HAL.
    5. Weng, Xi, 2015. "Can learning cause shorter delays in reaching agreements?," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 49-62.
    6. Ramsey, David M. & Szajowski, Krzysztof, 2008. "Selection of a correlated equilibrium in Markov stopping games," European Journal of Operational Research, Elsevier, vol. 184(1), pages 185-206, January.
    7. Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Eilon Solan & Nicolas Vieille, 2010. "Computing uniformly optimal strategies in two-player stochastic games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 237-253, January.
    9. 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.
    10. Vieille, Nicolas, 2002. "Stochastic games: Recent results," 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 48, pages 1833-1850 Elsevier.
    11. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    12. Shiran Rachmilevitch, 2016. "Symmetry and approximate equilibria in games with countably many players," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 709-717, August.
    13. Kimmo Berg, 2016. "Elementary Subpaths in Discounted Stochastic Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 304-323, September.
    14. Eilon Solan, 2005. "Subgame-Perfection in Quitting Games with Perfect Information and Differential Equations," Mathematics of Operations Research, INFORMS, vol. 30(1), pages 51-72, February.
    15. János Flesch & Arkadi Predtetchinski, 2016. "On refinements of subgame perfect $$\epsilon $$ ϵ -equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(3), pages 523-542, August.
    16. Rachmilevitch, Shiran, 2016. "Approximate equilibria in strongly symmetric games," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 52-57.
    17. Robert Samuel Simon, 2016. "The challenge of non-zero-sum stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 191-204, March.
    18. 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.
    19. Michael Ludkovski, 2010. "Stochastic Switching Games and Duopolistic Competition in Emissions Markets," Papers 1001.3455, arXiv.org, revised Aug 2010.
    20. Paul Schweinzer, 2003. "Dissolving a Common Value Partnership in a Repeated 'queto' Game," Discussion Paper Series dp318, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    21. Guo, Ivan & Rutkowski, Marek, 2016. "Discrete time stochastic multi-player competitive games with affine payoffs," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 1-32.

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