ABSTRACT
In the present paper, we consider a bio-economic equilibrium model which describes the dynamics of a fish population fished by several fishermen seeking to maximize their profits. Each fisherman tries to find the fishing effort which maximizes his profit at biological equilibrium without any consultation with others, but all of them have to respect two constraints: (1) the sustainable management of the resources ; and (2) the preservation of the biodiversity. With all these considerations, our problem leads to a generalized Nash equilibrium problem. The objective is to show that even when a fisherman (i) provides a fishing effort equal to twice the fishing effort of a fisherman (j), then the profit of fisherman (i) is not necessarily double that of fisherman (j).
Subject(s)
Fisheries , Game Theory , Models, EconomicABSTRACT
The evolution of dispersal is examined by looking at evolutionarily stable strategies (ESS) for dispersal parameters in discrete time multisite models without any cost of dispersal. ESS are investigated analytically, based on explicit results on sensitivity analysis of matrix models. The basic model considers an arbitrary number of sites and a single age class. An ESS for dispersal parameters is obtained when the spatial reproductive values, calculated at the density-dependent population equilibrium, are equal across sites. From this basic formulation, one derives equivalently that all local populations should be at equilibrium in the absence of migration, and that dispersal between sites should be balanced, i.e., the numbers of individuals arriving to and leaving a site are equal. These results are then generalized to a model with several age classes. Equal age-specific reproductive values do not however imply balanced dispersal in this case. Our results generalize to any number of sites and age classes those available ¿M. Doebeli, Dispersal and dynamics, Theoret. Popul. 47 (1995) 82 for two sites and one age class.
