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

Listed author(s):
  • Anna Krasnosielska-Kobos


  • Elżbieta Ferenstein


Registered author(s):

    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

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    Article provided by Springer in its journal Dynamic Games and Applications.

    Volume (Year): 3 (2013)
    Issue (Month): 2 (June)
    Pages: 220-235

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    Handle: RePEc:spr:dyngam:v:3:y:2013:i:2:p:220-235
    DOI: 10.1007/s13235-012-0070-7
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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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