Fish wars and cooperation maintenance

In this paper, a discrete-time game model related to a bioresource management problem (fish catching) is considered. We divide a fishery into regions, which are exploited by single players. The center (referee) shares a reservoir between the competitors. The players (countries), which harvest the fish stock are the participants of this game.We assume that there are migratory exchanges between the regions of the reservoir. Therefore, the stock in one region depends not only on the previous stock and catch in the region, but also on the stock and catch in neighboring regions. We derive the Nash and cooperative equilibria for an infinite planning horizon.We consider two ways to maintain the cooperation: incentive equilibrium and time-consistent imputation distribution procedure. We investigate the cooperative incentive equilibrium in the case when the center punishes players for a deviation.Also we consider the case when the center is a player and find the Shapley value and time-consistent imputation distribution procedure. We introduce a new condition which offers an incentive to players to keep cooperating.