Sole owner harvesting policies under the threat of entry: A two-stage linear game

Abstract

In this paper, we analyze harvesting policies for a producer who is guaranteed exclusive harvesting rights to a renewable resource for a specified period of time. A second producer may enter the market after these rights have expired and if entry occurs, the duopoly stage is modeled as a noncooperative differential game. We assume that the price and average costs are constant and that the harvest rate is linearly dependent upon the stock level and the effort expended. After the solution to the duopoly game is presented, we give the solution to the two-stage profit maximization problem of the incumbent. A modified most rapid approach path solution is shown to be optimal under certain conditions.