Tipping and strong rarity value in a stochastic fishery game

Strong rarity value is the phenomenon that an increase in scarcity of a species (of plants or animals) leads to a price increase which more than compensates increased search costs and lower numbers found or caught. Tipping here is a regime shift moving the system into a low resource-level state from which it is impossible to escape unless measures to restore the resource are taken for a long period of time. We engineer a model in which agents wishing to maximize their limiting average rewards have two choices at every stage of the play, restraint or no-restraint (“overfish”). Overfishing damages the resource, causes tipping and induces scarcity which in turn creates rarity value. We find that Pareto-efficient equilibrium outcomes for very patient agents may require substantial overexploitation of the resource inducing serious threats to its sustainability. However, equilibrium behavior yields a sufficiently rich scheme of outcomes that leave room for viable compromises between ecologically and economically maximalistic policies.