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A Differential Game with Exit Costs

Author

Listed:
  • Fabio Bagagiolo

    (University of Trento)

  • Rosario Maggistro

    (Ca’ Foscari University of Venice)

  • Marta Zoppello

    (Politecnico di Torino)

Abstract

We study a differential game where two players separately control their own dynamics, pay a running cost, and moreover pay an exit cost (quitting the game) when they leave a fixed domain. In particular, each player has its own domain and the exit cost consists of three different exit costs, depending whether either the first player only leaves its domain, or the second player only leaves its domain, or they both simultaneously leave their own domain. We prove that, under suitable hypotheses, the lower and upper values are continuous and are, respectively, the unique viscosity solution of a suitable Dirichlet problem for a Hamilton–Jacobi–Isaacs equation. The continuity of the values relies on the existence of suitable non-anticipating strategies respecting the domain constraint. This problem is also treated in this work.

Suggested Citation

  • Fabio Bagagiolo & Rosario Maggistro & Marta Zoppello, 2020. "A Differential Game with Exit Costs," Dynamic Games and Applications, Springer, vol. 10(2), pages 297-327, June.
    • Handle: RePEc:spr:dyngam:v:10:y:2020:i:2:d:10.1007_s13235-019-00334-y
    DOI: 10.1007/s13235-019-00334-y
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    References listed on IDEAS

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    1. Piernicola Bettiol & Pierre Cardaliaguet & Marc Quincampoix, 2006. "Zero-sum state constrained differential games: existence of value for Bolza problem," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(4), pages 495-527, November.
    2. R. Buckdahn & P. Cardaliaguet & M. Quincampoix, 2011. "Some Recent Aspects of Differential Game Theory," Dynamic Games and Applications, Springer, vol. 1(1), pages 74-114, March.
    3. repec:dau:papers:123456789/6046 is not listed on IDEAS
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