Strong and weak rarity value in Small Fish Wars

We analyze the effects of rarity value on the economic and ecological sustainability of a natural resource. Rarity value means that under extreme scarcity of the resource unit profits increase 'explosively'. We focus on equilibrium behavior of very patient agents in a Small Fish War. In such a setting, agents interacting on a body of water have two options: they can fish with restraint or without. Fishing with restraint allows the fish stock to recover; fishing without yields higher immediate but lower future catches. We make a distinction between weak and strong rarity value. In the weak variant, equilibrium behavior induces high sustainable fish stocks and long-run yields. In the strong one, very high equilibrium rewards may be obtained by almost exhausting the resource, but more moderate equilibrium rewards are feasible without endangering sustainability.