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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
    1. M. I. Taksar, 1985. "Average Optimal Singular Control and a Related Stopping Problem," Mathematics of Operations Research, INFORMS, vol. 10(1), pages 63-81, February.
    2. Pui Chan Lon & Mihail Zervos, 2011. "A Model for Optimally Advertising and Launching a Product," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 363-376, May.
    3. Tiziano De Angelis & Giorgio Ferrari & John Moriarty, 2014. "A Non Convex Singular Stochastic Control Problem and its Related Optimal Stopping Boundaries," Papers 1405.2442, arXiv.org, revised Nov 2014.
    4. Boetius, Frederik & Kohlmann, Michael, 1998. "Connections between optimal stopping and singular stochastic control," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 253-281, September.
    5. H. Dharma Kwon & Hongzhong Zhang, 2015. "Game of Singular Stochastic Control and Strategic Exit," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 869-887, October.
    6. Kerry Back & Dirk Paulsen, 2009. "Open-Loop Equilibria and Perfect Competition in Option Exercise Games," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4531-4552, November.
    7. Alvarez, Luis H. R., 2000. "Singular stochastic control in the presence of a state-dependent yield structure," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 323-343, April.
    8. Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
    9. De Angelis, Tiziano & Ferrari, Giorgio, 2014. "A stochastic partially reversible investment problem on a finite time-horizon: Free-boundary analysis," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4080-4119.
    10. de Angelis, Tiziano & Ferrari, Giorgio, 2014. "A Stochastic Reversible Investment Problem on a Finite-Time Horizon: Free Boundary Analysis," Center for Mathematical Economics Working Papers 477, Center for Mathematical Economics, Bielefeld University.
    11. Frederick Ploeg & Aart Zeeuw, 1992. "International aspects of pollution control," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 2(2), pages 117-139, March.
    12. Guo, Xin & Pham, Huyên, 2005. "Optimal partially reversible investment with entry decision and general production function," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 705-736, May.
    13. Jorgensen, Steffen & Zaccour, Georges, 2001. "Time consistent side payments in a dynamic game of downstream pollution," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1973-1987, December.
    14. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Giorgio Ferrari & Torben Koch, 2019. "On a strategic model of pollution control," Annals of Operations Research, Springer, vol. 275(2), pages 297-319, April.
    5. Tiziano De Angelis & Erik Ekstrom, 2016. "The dividend problem with a finite horizon," Papers 1609.01655, arXiv.org, revised Nov 2017.

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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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