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

Mojtaba Dehghan Banadaki and Hamidreza Navidi
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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

Games, 2020, vol. 11, issue 3, 1-11

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 (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2020
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