Dynamic Modeling of the Harvesting Function: The Conflicting Case

This paper is concerned with the classic topic of intertemporal resource economics: the optimal harvesting of renewable natural resources over time by one and several resource extractors with conflicting interests. The traditional management model, dating back to Plourde [1], is overlooked both in the simple case for which the resource stock is treated as a state variable and in the improved case for which the harvesting equipment is treated as a stock variable. As a result in the extended case, the equilibrium richer than the saddle point, with bifurcations and limit cycles, is possible. While the results of the enriched management case are consistent with the concept of the pulse fishing, as this concept is introduced by Clark [2]-[4], in the conflicting case the conditions, under which the richer limit cycle equilibrium occurs, are not enough investigated. Therefore, we discuss conflicts as a game with two types of players involved: the traditional fishermen armed with the basic equipment and the heavy equipment users. Both players have a common depletion function, considered as harvesting, which is dependent together on personal effort and on intensity of equipment’s usage.