Incentive equilibrium in discrete-time bioresource sharing model

A discrete-time game model related to the bioresource management problem (fish catching) is considered. Nash and cooperative equilibria for an infinite planning horizon is derived. Solutions of the infinite-time problem are obtained by finding solutions of n-step game and letting the horizon tend to infinity. The water area is divided into two parts, s and 1-s, where two countries exploit the fish stock. The utility functions of the countries are assumed to be logarithmic. A cooperative equilibrium by using the same approach of transfer from the finite to infinite resource management problem is found. Here, the players wish to maximize the discounted sum of their total utilities on the infinite time horizon. The concept of incentive equilibrium gives us the condition that the maximum must be achieved at cooperative equilibrium. In such a way, an incentive equilibrium for both players in the n-step game is found and, then, for an infinite time planning horizon.