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Volume 11
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Article

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

by
Mojtaba Dehghan Banadaki
and
Hamidreza Navidi
*
Department of Applied Mathematics, Shahed University, Tehran P.O. Box 18151-159, Iran
*
Author to whom correspondence should be addressed.
Games 2020, 11(3), 28; https://doi.org/10.3390/g11030028
Submission received: 28 February 2020 / Revised: 6 April 2020 / Accepted: 9 April 2020 / Published: 23 July 2020
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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.
Keywords: differential game theory; open-loop Nash equilibrium; Pontryagin’s maximum principle; Tau method; bioeconomics differential game theory; open-loop Nash equilibrium; Pontryagin’s maximum principle; Tau method; bioeconomics

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MDPI and ACS Style

Dehghan Banadaki, M.; Navidi, H. Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method. Games 2020, 11, 28. https://doi.org/10.3390/g11030028

AMA Style

Dehghan Banadaki M, Navidi H. Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method. Games. 2020; 11(3):28. https://doi.org/10.3390/g11030028

Chicago/Turabian Style

Dehghan Banadaki, Mojtaba, and Hamidreza Navidi. 2020. "Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method" Games 11, no. 3: 28. https://doi.org/10.3390/g11030028

APA Style

Dehghan Banadaki, M., & Navidi, H. (2020). Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method. Games, 11(3), 28. https://doi.org/10.3390/g11030028

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