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Quitting Games - An Example

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  • Eilon Solan
  • Nicholas Vieille

Abstract

Quitting games are multi-player sequential games in which, at every stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; each player i then receives a payoff r S i, which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is zero.¶ We exhibit a four-player quitting game, where the "simplest" equilibrium is periodic with period two. We argue that this implies that all known methods to prove existence of an equilibrium payoff in multi-player stochastic games are therefore bound to fail in general, and provide some geometric intuition for this phenomenon.
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  • Eilon Solan & Nicholas Vieille, 2001. "Quitting Games - An Example," Discussion Papers 1314, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    • Handle: RePEc:nwu:cmsems:1314
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/6017 is not listed on IDEAS
    2. Eilon Solan & Nicolas Vieille, 1998. "Quitting Games," Discussion Papers 1227, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Nicolas Vieille, 2000. "Two-player stochastic games I: A reduction," Post-Print hal-00481401, HAL.
    4. J. Flesch & F. Thuijsman & O. J. Vrieze, 1996. "Recursive Repeated Games with Absorbing States," Mathematics of Operations Research, INFORMS, vol. 21(4), pages 1016-1022, November.
    5. Eilon Solan, 1999. "Three-Player Absorbing Games," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 669-698, August.
    6. Nicolas Vieille, 2000. "Two-player stochastic games II: The case of recursive games," Post-Print hal-00481416, HAL.
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    Cited by:

    1. Robert Samuel Simon, 2012. "A Topological Approach to Quitting Games," Mathematics of Operations Research, INFORMS, vol. 37(1), pages 180-195, February.
    2. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
    3. Ayala Mashiah-Yaakovi, 2015. "Correlated Equilibria in Stochastic Games with Borel Measurable Payoffs," Dynamic Games and Applications, Springer, vol. 5(1), pages 120-135, March.
    4. Kimmo Berg, 2016. "Elementary Subpaths in Discounted Stochastic Games," Dynamic Games and Applications, Springer, vol. 6(3), pages 304-323, September.
    5. Shmaya, Eran & Solan, Eilon & Vieille, Nicolas, 2003. "An application of Ramsey theorem to stopping games," Games and Economic Behavior, Elsevier, vol. 42(2), pages 300-306, February.
    6. Weng, Xi, 2015. "Can learning cause shorter delays in reaching agreements?," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 49-62.
    7. 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.
    8. Elżbieta Ferenstein, 2007. "Randomized stopping games and Markov market games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 531-544, December.
    9. Rachmilevitch, Shiran, 2016. "Approximate equilibria in strongly symmetric games," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 52-57.
    10. Eilon Solan & Omri N. Solan, 2020. "Quitting Games and Linear Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 45(2), pages 434-454, May.
    11. 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.
    12. Nie, Tianyang & Rutkowski, Marek, 2014. "Multi-player stopping games with redistribution of payoffs and BSDEs with oblique reflection," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2672-2698.

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    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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