Multistage model for renewable resource exploitation by the players of two types

Denis V. Kuzyutin^a, Nadezhda V. Smirnova^b, Igor R. Tantlevskij<sup>a

a</sup> Saint-Petersburg State University
^b HSE University

Abstract: The paper examines an infinite-horizon multistage game of renewable resource extraction with two types of players, differing in the discount rates of future payoffs. Using the dynamic programming method, a non-cooperative solution - a subgame perfect Nash equilibrium in stationary positional strategies, as well as a cooperative (Pareto-optimal) solution for the case of complete cooperation of all players were constructed. The resulting solutions were analyzed for sensitivity to changes in the model parameters, in particular, the range for the coefficient of natural resource renewal was found, in which a non-cooperative solution leads to complete depletion of the resource, while a cooperative scheme allows to avoid such a negative scenario. A numerical example is given to demonstrate the theoretical results obtained.

Keywords: multistage game, renewable resources, asymmetric players, Nash equilibria, cooperative solution, sensitivity analysis.

UDC: 519.837
BBK: 22.18

Received: 31.10.2023
Revised: 25.12.2023
Accepted: 01.03.2024