A Mathematical Model of Overfishing: Replenishable Resources and Social Dilemma

Abstract

The catchable stock of fish enjoys natural processes of replenishment, but is often exposed to a crisis of diminution or depletion because of overfishing by human beings. The present paper sets up a model of a situation where, under a certain mechanism of replenishment, players(= fishermen) are offered binary choices: overfishing and moderate fishing. We showed that fishing activities turn out to be ‘social dilemma’ in the sense formulated by R. Dawes under specific parametric conditions involving replenishment and fishing strategies. We also examined sociological implications of the model in terms of PD (prisoner's dilemma) game. © 1989, Japanese Association For Mathematical Sociology. All rights reserved.