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Exit game with private information

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  • H. Dharma Kwon
  • Jan Palczewski

Abstract

The timing of strategic exit is one of the most important but difficult business decisions, especially under competition and uncertainty. Motivated by this problem, we examine a stochastic game of exit in which players are uncertain about their competitor's exit value. We construct an equilibrium for a large class of payoff flows driven by a general one-dimensional diffusion. In the equilibrium, the players employ sophisticated exit strategies involving both the state variable and the posterior belief process. These strategies are specified explicitly in terms of the problem data and a solution to an auxiliary optimal stopping problem. The equilibrium we obtain is further shown to be unique within a wide subclass of symmetric Bayesian equilibria.

Suggested Citation

  • H. Dharma Kwon & Jan Palczewski, 2022. "Exit game with private information," Papers 2210.01610, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2210.01610
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    References listed on IDEAS

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    1. Georgiadis, George & Kim, Youngsoo & Kwon, H. Dharma, 2022. "The absence of attrition in a war of attrition under complete information," Games and Economic Behavior, Elsevier, vol. 131(C), pages 171-185.
    2. Riedel, Frank & Steg, Jan-Henrik, 2017. "Subgame-perfect equilibria in stochastic timing games," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 36-50.
    3. Daniel W. Elfenbein & Anne Marie Knott, 2015. "Time to exit: Rational, behavioral, and organizational delays," Strategic Management Journal, Wiley Blackwell, vol. 36(7), pages 957-975, July.
    4. De Angelis, Tiziano & Ekström, Erik, 2020. "Playing with ghosts in a Dynkin game," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6133-6156.
    5. Fabien Gensbittel & Christine Grün, 2019. "Zero-Sum Stopping Games with Asymmetric Information," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 277-302, February.
    6. Steg, Jan-Henrik, 2015. "Symmetric equilibria in stochastic timing games," Center for Mathematical Economics Working Papers 543, Center for Mathematical Economics, Bielefeld University.
    7. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, December.
    8. Pauli Murto, 2004. "Exit in Duopoly Under Uncertainty," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 111-127, Spring.
    9. Tiziano De Angelis & Erik Ekstrom & Kristoffer Glover, 2018. "Dynkin games with incomplete and asymmetric information," Papers 1810.07674, arXiv.org, revised Jul 2020.
    10. Luis H. R. Alvarez, 2001. "Reward functionals, salvage values, and optimal stopping," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(2), pages 315-337, December.
    11. Fudenberg, Drew & Tirole, Jean, 1986. "A Theory of Exit in Duopoly," Econometrica, Econometric Society, vol. 54(4), pages 943-960, July.
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    Cited by:

    1. Décamps, Jean-Paul & Gensbittel, Fabien & Mariotti, Thomas, 2022. "Mixed-Strategy Equilibria in the War of Attrition under Uncertainty," TSE Working Papers 22-1374, Toulouse School of Economics (TSE), revised 22 Nov 2023.

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