Cooperative and non-cooperative behaviour in the exploitation of a common renewable resource with environmental stochasticity
Classical fisheries biology aims to optimise fisheries-level outcomes, such as yield or profit, by controlling the fishing effort. This can be adjusted to allow for the effects of environmental stochasticity, or noise, in the population dynamics. However, when multiple fishing entities, which could represent countries, commercial organisations, or individual vessels, can autonomously determine their own fishing effort, the the optimal action for one fishing entity depends on the actions of others. Coupled with noise in the population dynamics, and with decisions about fishing effort made repeatedly, this becomes an iterated stochastic game. We tackle this problem using the tools of stochastic optimisation, first for the monopolists problem and then for the duopolists problem. In each case, we derive optimal policies that specify the best level of fishing effort for a given stock biomass. Under these optimal policies, we can calculate the equilibrium stock biomass, the expected long-term return from fishing and the probability of stock collapse. We also show that there is a threshold stock biomass below which it is optimal to stop fishing until the stock recovers. We then develop an agent-based model to test the effectiveness of simple strategies for responding to deviations by an opponent from a cooperative fishing level. Our results show that the economic value of the fishery to a monopolist, or to a consortium of fishing agents, is robust to a certain level of noise. However, without the means of making agreements about fishing effort, even low levels of noise make sustained cooperation between autonomous fishing agents difficult.