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Construction of Nash Equilibrium in a Game Version of Elfving’s Multiple Stopping Problem

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  • Anna Krasnosielska-Kobos

    ()

  • Elżbieta Ferenstein

    ()

Abstract

Multi-person stopping games with players’ priorities are considered. Players observe sequentially offers Y 1 ,Y 2 ,… at jump times T 1 ,T 2 ,… of a Poisson process. Y 1 ,Y 2 ,… are independent identically distributed random variables. Each accepted offer Y n results in a reward G n =Y n r(T n ), where r is a non-increasing discount function. If more than one player wants to accept an offer, then the player with the highest priority (the lowest ordering) gets the reward. We construct Nash equilibrium in the multi-person stopping game using the solution of a multiple optimal stopping time problem with structure of rewards {G n }. We compare rewards and stopping times of the players in Nash equilibrium in the game with the optimal rewards and optimal stopping times in the multiple stopping time problem. It is also proved that presented Nash equilibrium is a Pareto optimum of the game. The game is a generalization of the Elfving stopping time problem to multi-person stopping games with priorities. Copyright The Author(s) 2013

Suggested Citation

  • Anna Krasnosielska-Kobos & Elżbieta Ferenstein, 2013. "Construction of Nash Equilibrium in a Game Version of Elfving’s Multiple Stopping Problem," Dynamic Games and Applications, Springer, vol. 3(2), pages 220-235, June.
  • Handle: RePEc:spr:dyngam:v:3:y:2013:i:2:p:220-235
    DOI: 10.1007/s13235-012-0070-7
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    References listed on IDEAS

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    1. Gershkov, Alex & Moldovanu, Benny, 2010. "Efficient sequential assignment with incomplete information," Games and Economic Behavior, Elsevier, vol. 68(1), pages 144-154, January.
    2. S. Christian Albright, 1974. "Optimal Sequential Assignments with Random Arrival Times," Management Science, INFORMS, vol. 21(1), pages 60-67, September.
    3. Krasnosielska, Anna, 2009. "A version of the Elfving problem with random starting time," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2429-2436, December.
    4. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
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    Cited by:

    1. Anna Krasnosielska-Kobos, 2016. "Construction of Nash equilibrium based on multiple stopping problem in multi-person game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 53-70, February.

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