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Continuous unplanned consumption of renewable resources (e.g., fish) could lead to their extinction. A two-country single-renewable-resource dynamic model is formulated in a differential game-theoretic framework. A competitive market consumer benefit function is used as an objective function to be maximized by each country, subject to the resource population/growth/catch dynamics. The optimal competitive catch strategies are derived, and their economic implications are discussed. It is shown that, in general, the optimal catch strategies are not always competitive. Possibilities for each country to be idle or to apply an optimal (monopolistic) catch strategy are also feasible.