Appropriation of common access natural resources through exploration: A differential game of a claiming rush

This paper provides a model of natural resource exploration, where the sole motivation to explore arises from a strategic incentive to preempt competitors. It is assumed that private ownership rights over a finite unexplored and commonly held resource stock can be established through a costly deterministic exploration process. The open-loop and the feedback Nash equilibrium is analysed. It is shown that in between intervals of soaring exploratory activities there may be an interval where exploration is declining over time.