A Duopoly with Common Renewable Resource and Incentives

In this paper, we study a duopoly model in which two symmetric firms exploit the same public renewable resource as an input for the production of a homogeneous good. We consider the case where the firms are provided with public incentives in order to prevent the resource exhaustion in a finite time horizon which coincides with the harvesting-license period. As a consequence, we consider a differential game in finite time horizon and compute the Open Loop and linear Feedback Nash Equilibria of the game. We study the social welfare and the optimal incentives polices derived from the solutions.

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

Games ◽

10.3390/g11030028 ◽

2020 ◽

Vol 11 (3) ◽

pp. 28

Author(s):

Mojtaba Dehghan Banadaki ◽

Hamidreza Navidi

Keyword(s):

Differential Game ◽

Time Horizon ◽

Renewable Resource ◽

Open Loop ◽

Tau Method ◽

Point Boundary ◽

Algebraic Equations ◽

Runge Kutta Method ◽

Finite Time Horizon ◽

Nash Differential Games

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.

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Numerical Versus Analytic Calculation of Optima and Equilibria in Fish Wars Model with Finite Time Horizon

SSRN Electronic Journal ◽

10.2139/ssrn.2778639 ◽

2016 ◽

Author(s):

Agnieszka Wiszniewska-Matyszkiel ◽

Rajani Singh

Keyword(s):

Finite Time ◽

Time Horizon ◽

Analytic Calculation ◽

Finite Time Horizon

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A Constrained Markovian Diffusion Model for Controlling the Pollution Accumulation

Mathematics ◽

10.3390/math9131466 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1466

Author(s):

Beatris Adriana Escobedo-Trujillo ◽

José Daniel López-Barrientos ◽

Javier Garrido-Meléndez

Keyword(s):

Dynamic Programming ◽

Dirichlet Problem ◽

Stochastic Control ◽

Finite Time ◽

Time Horizon ◽

Closed Loop ◽

Programming Techniques ◽

Pollution Accumulation ◽

Finite Time Horizon ◽

The Cost

This work presents a study of a finite-time horizon stochastic control problem with restrictions on both the reward and the cost functions. To this end, it uses standard dynamic programming techniques, and an extension of the classic Lagrange multipliers approach. The coefficients considered here are supposed to be unbounded, and the obtained strategies are of non-stationary closed-loop type. The driving thread of the paper is a sequence of examples on a pollution accumulation model, which is used for the purpose of showing three algorithms for the purpose of replicating the results. There, the reader can find a result on the interchangeability of limits in a Dirichlet problem.

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