A Game Theoretical Coalition Model of International Fishing with Time Delay

Abstract

The oligopoly model of international fishing of Szidarovszky and Okuguchi [7] where the harvesting countries form a coalition is revisited with the additional assumption that there is a time lag in obtaining and implementing information on the fish stock. The introduction of continuously distributed time lags results in a special Volterra-type integro-differential equation. Since it is equivalent to a system of nonlinear ordinary differential equations, linearization and standard techniques are used to examine the local asymptotic behavior of the equilibrium. Stability conditions are derived and in the case of instability special cyclic behavior is analyzed.