Multistage Model for Renewable Resource Extraction by Players of Two Types

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, we construct a noncooperative solution—a subgame perfect Nash equilibrium in stationary feedback strategies—and a cooperative (Pareto optimal) solution for the case of complete cooperation of all players. The resulting solutions are analyzed for sensitivity to variations in model parameters. In particular, the range of the coefficient of natural resource renewal is found in which a noncooperative solution leads to complete depletion of the resource, while a cooperative scheme allows the players to avoid this negative scenario. A numerical example is given to demonstrate the theoretical results obtained.