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Potential Differential Games

Author

Listed:
  • Alejandra Fonseca-Morales

    (CINVESTAV-IPN)

  • Onésimo Hernández-Lerma

    (CINVESTAV-IPN)

Abstract

This paper introduces the notion of a potential differential game (PDG), which roughly put is a noncooperative differential game to which we can associate an optimal control problem (OCP) whose solutions are Nash equilibria for the original game. If this is the case, there are two immediate consequences. Firstly, finding Nash equilibria for the game is greatly simplified, because it is a lot easier to deal with an OCP than with the original game itself. Secondly, the Nash equilibria obtained from the associated OCP are automatically “pure” (or deterministic) rather than “mixed” (or randomized). We restrict ourselves to open-loop differential games. We propose two different approaches to identify a PDG and to construct a corresponding OCP. As an application, we consider a PDG with a certain turnpike property that is obtained from results for the associated OCP. We illustrate our results with a variety of examples.

Suggested Citation

  • Alejandra Fonseca-Morales & Onésimo Hernández-Lerma, 2018. "Potential Differential Games," Dynamic Games and Applications, Springer, vol. 8(2), pages 254-279, June.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:2:d:10.1007_s13235-017-0218-6
    DOI: 10.1007/s13235-017-0218-6
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    References listed on IDEAS

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    1. Rabah Amir & Niels Nannerup, 2006. "Information Structure and the Tragedy of the Commons in Resource Extraction," Journal of Bioeconomics, Springer, vol. 8(2), pages 147-165, August.
    2. D. Dragone & L. Lambertini & G. Leitmann & A. Palestini, 2008. "Hamiltonian potential functions for differential games," Working Papers 644, Dipartimento Scienze Economiche, Universita' di Bologna.
    3. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190, September.
    4. Slade, Margaret E, 1994. "What Does an Oligopoly Maximize?," Journal of Industrial Economics, Wiley Blackwell, vol. 42(1), pages 45-61, March.
    5. Ngo Long, 2011. "Dynamic Games in the Economics of Natural Resources: A Survey," Dynamic Games and Applications, Springer, vol. 1(1), pages 115-148, March.
    6. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701, September.
    7. Nico Tauchnitz, 2015. "The Pontryagin Maximum Principle for Nonlinear Optimal Control Problems with Infinite Horizon," Journal of Optimization Theory and Applications, Springer, vol. 167(1), pages 27-48, October.
    8. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, September.
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