Pricing of Natural Resource under a Randomly Furcating Environment

Abstract

Research into the optimal exploitation and pricing of renewable resources in the framework of dynamic games began with the pioneering work of Levhari and Mirman in the 1980s. Since that time, the dynamic game theoretic approach has become increasingly popular in the analysis of common property resource extraction and evaluation. This paper relaxes a number of traditional assumptions and introduces the fundamental idea that inherently, the future environment under which natural resources are extracted and priced is not known with certainty, especially in the sense that different patterns of events can occur sequentially with different probabilities over time. A model of a resource pricing dynamic game is then presented, in which the future payoffs and the evolution of the resource stock dynamics are uncertain in the sense that the underlying stochastic processes display a random furcating property. The Nash equilibria are obtained, together with interesting implications for the analysis of resource pricing. On a more general level, this new approach widens the application of differential game theory to problems in which an inherently uncertain future environment evolves sequentially in a branching pattern over time.