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Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method

Author

Listed:
  • Mojtaba Dehghan Banadaki

    (Department of Applied Mathematics, Shahed University, Tehran P.O. Box 18151-159, Iran)

  • Hamidreza Navidi

    (Department of Applied Mathematics, Shahed University, Tehran P.O. Box 18151-159, Iran)

Abstract

In this paper, an efficient implementation of the Tau method is presented for finding the open-loop Nash equilibrium of noncooperative nonzero-sum two-player differential game problems with a finite-time horizon. Regarding this approach, the two-point boundary value problem derived from Pontryagin’s maximum principle is reduced to a system of algebraic equations that can be solved numerically. Finally, a differential game arising from bioeconomics among firms harvesting a common renewable resource is included to illustrate the accuracy and efficiency of the proposed method and a comparison is made with the result obtained by fourth order Runge–Kutta method.

Suggested Citation

  • Mojtaba Dehghan Banadaki & Hamidreza Navidi, 2020. "Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method," Games, MDPI, vol. 11(3), pages 1-11, July.
    • Handle: RePEc:gam:jgames:v:11:y:2020:i:3:p:28-:d:388591
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    References listed on IDEAS

    as
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