Strong rarity value in view of hysteresis in a stochastic fishery game

Strong rarity value is the phenomenon that an increase in scarcity of a species leads to a price increase which more than compensates increased search costs and decreased landings. Hysteresis here can be seen as a regime shift in which overfishing moves the system into a stable low resource-level state. Measures to restore the resource may take a long time for the system to move out of this state again.
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 (`overfishing'). Overfishing damages the resource and causes hysteresis to occur. The former induces scarcity which in turn creates scarcity value, and hysteresis makes it hard for the resource to recover.
Results show that Pareto efficient equilibrium outcomes for very patient agents may require substantial overexploitation of the resource which induces serious threats to the sustainability of the resource. Incentives of patient agents and very impatient ones (not modeled here) may point in the same direction, namely ruthless exploitation, which requires a careful long term management.