Sharing a Fish Stock When Distribution and Harvest Costs are Density Dependent

Abstract

We studied cooperative and competitive solutions for managing a trans-boundary fish stock that has a stock-size dependent distribution and harvesting costs, using Norwegian spring-spawning (NSS) herring (Clupea harengus) as a case study. This is among the first studies to investigate the effect of a dynamic distribution in a partition function game framework, i.e., including externalities. The special feature of NSS herring is that it comes under the sole ownership of Norway when the stock size is sufficiently low. The three players in our game are differentiated by stock ownership, cost per unit effort and stock elasticity of harvest. We find that cost asymmetry improves the likelihood of forming a stable grand coalition as harvesting load can be assigned to each fishing zone according to a player’s relative cost level and the density of fish. A dynamic distribution increases the bargaining power of Norway because of her ability to control both the total stock and the stock shares in different zones, especially during the stock transition years. However, the bargaining power of Norway may disappear if her cost of harvesting exceeds that of the other players. This loss of bargaining power can take on two forms: first, a dynamic distribution may encourage a minor player to free ride because Norway, needing a coalition partner to improve her cost-effectiveness, would be less inclined to retaliate as retaliation hurts her ally as much as the free-rider; second, in a stable grand coalition, Norway is not guaranteed to receive an allocation of benefit shares in proportion to (not to say in excess of) her stock ownership. At the current stock condition, the strategy where Norway reduces stock abundance below the level where the stock becomes non-migratory is found attractive only if the discounting rate is sufficiently high.