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Construction of Nash equilibrium based on multiple stopping problem in multi-person game

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  • Anna Krasnosielska-Kobos

    (Warsaw University of Technology)

Abstract

We consider a multi-person stopping game with players’ priorities and multiple stopping. Players observe sequential offers at random or fixed times. Each accepted offer results in a reward. Each player can obtain fixed number of rewards. If more than one player wants to accept an offer, then the player with the highest priority among them obtains it. The aim of each player is to maximize the expected total reward. For the game defined this way, we construct a Nash equilibrium. The construction is based on the solution of an optimal multiple stopping problem. We show the connections between expected rewards and stopping times of the players in Nash equilibrium in the game and the optimal expected rewards and optimal stopping times in the multiple stopping problem. A Pareto optimum of the game is given. It is also proved that the presented Nash equilibrium is a sub-game perfect Nash equilibrium. Moreover, the Nash equilibrium payoffs are unique. We also present new results related to multiple stopping problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:83:y:2016:i:1:d:10.1007_s00186-015-0519-8
    DOI: 10.1007/s00186-015-0519-8
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    References listed on IDEAS

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    1. Solan, Eilon & Vieille, Nicolas, 2003. "Deterministic multi-player Dynkin games," Journal of Mathematical Economics, Elsevier, vol. 39(8), pages 911-929, November.
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    4. 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.
    5. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
    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.
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    Cited by:

    1. Georgy Yu. Sofronov, 2020. "An Optimal Double Stopping Rule for a Buying-Selling Problem," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 1-12, March.
    2. Georgy Sofronov, 2020. "An Optimal Decision Rule for a Multiple Selling Problem with a Variable Rate of Offers," Mathematics, MDPI, vol. 8(5), pages 1-11, May.

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