In a non-cooperative game, the players look for the best response to what they think the other players will do. This chapter deals with a simple two-country model, applying the Nash-Cournot approach as in Clark and Levhari and Mirman. In this setting, 'bad' outcomes, and possibly total annihilation of the fish stock, are likely to occur unless one country is sufficiently dominant. To obtain a non-cooperative solution with a viable stock, one country must have a sufficiently large share of the stock to provide an incentive for conservation. The chapter discusses this critical share for the case of stock-independent cost per unit of fish caught, a case where stock extinction can result from a non-cooperative play. In a multi-country setting, one country is less likely to be sufficiently dominant, and hence stock extinction would seem all the more likely.