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

Mojtaba Dehghan Banadaki | Hamid Navidi Ghaziani

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=137735
Date :  2020/07/23
Publish in :    Games
DOI :  https://doi.org/10.3390/g11030028
Link :  https://www.mdpi.com/2073-4336/11/3/28/htm
Keywords :differential game theory; open-loop Nash equilibrium; Pontryagin’s maximum principle;Tau method; bioeconomics

Abstract :

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In this paper, an efficient implementation of the Tau method is presented for finding theopen-loop Nash equilibrium of noncooperative nonzero-sum two-player differential game problemswith a finite-time horizon. Regarding this approach, the two-point boundary value problem derivedfrom Pontryagin’s maximum principle is reduced to a system of algebraic equations that can besolved numerically. Finally, a differential game arising from bioeconomics among firms harvestinga common renewable resource is included to illustrate the accuracy and efficiency of the proposedmethod and a comparison is made with the result obtained by fourth order Runge–Kutta method. (17) (PDF) Numerical Solution of Open-Loop Nash Differential Games Based on the Legendre Tau Method. Available from: https://www.researchgate.net/publication/343170978_Numerical_Solution_of_Open-Loop_Nash_Differential_Games_Based_on_the_Legendre_Tau_Method accessed Aug 18 2020.