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Stochastic nonzero-sum games: a new connection between singular control and optimal stopping

Author

Listed:
  • de Angelis, Tiziano

    (Center for Mathematical Economics, Bielefeld University)

  • Ferrari, Giorgio

    (Center for Mathematical Economics, Bielefeld University)

Abstract

In this paper we establish a new connection between a class of 2-player nonzerosum games of optimal stopping and certain 2-player nonzero-sum games of singular control. We show that whenever a Nash equilibrium in the game of stopping is attained by hitting times at two separate boundaries, then such boundaries also trigger a Nash equilibrium in the game of singular control. Moreover a differential link between the players' value functions holds across the two games.

Suggested Citation

  • de Angelis, Tiziano & Ferrari, Giorgio, 2016. "Stochastic nonzero-sum games: a new connection between singular control and optimal stopping," Center for Mathematical Economics Working Papers 565, Center for Mathematical Economics, Bielefeld University.
    • Handle: RePEc:bie:wpaper:565
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    File URL: https://pub.uni-bielefeld.de/download/2904753/2904755
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    References listed on IDEAS

    as
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    Cited by:

    1. Ferrari, Giorgio, 2018. "On a Class of Singular Stochastic Control Problems for Reflected Diffusions," Center for Mathematical Economics Working Papers 592, Center for Mathematical Economics, Bielefeld University.
    2. Tiziano De Angelis & Erik Ekstrom, 2016. "The dividend problem with a finite horizon," Papers 1609.01655, arXiv.org, revised Nov 2017.
    3. Giorgio Ferrari & Torben Koch, 2019. "On a strategic model of pollution control," Annals of Operations Research, Springer, vol. 275(2), pages 297-319, April.
    4. Xin Guo & Wenpin Tang & Renyuan Xu, 2018. "A class of stochastic games and moving free boundary problems," Papers 1809.03459, arXiv.org, revised Oct 2021.
    5. Ferrari, Giorgio & Koch, Torben, 2018. "On a Strategic Model of Pollution Control," Center for Mathematical Economics Working Papers 586, Center for Mathematical Economics, Bielefeld University.

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    More about this item

    Keywords

    games of singular control; games of optimal stopping; Nash equilibrium; onedimensional diffusion; Hamilton-Jacobi-Bellman equation; verification theorem;
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