The sharing of a migrating fish stock between two players is considered. Data on the Northeast Atlantic mackerel are used to model the fishery. A growth function is estimated, and random fluctuations in growth and recruitment are used to simulate the fishery. Three different migration models are considered: i) deterministic, ii) stock-dependent, and iii) purely random. With deterministic migrations, the minor player has a disproportionate bargaining strength and must be offered a relatively large share of a cooperative solution. The minor player's bargaining strength is weak if the migrations into his economic zone are stock-dependent, but strong if they are purely random. The risk of extinction is shown to be high without stock-dependent unit cost of fish, and to get a viable Nash-Cournot equilibrium the major player's share must be well above one half.

JEL Classification Codes: Q22, Q28, C72