Motivated by recent examples, this study proposes a dynamic multistage optimal control problem to explain the instability of International Fishery Agreements (IFAs). We model two heterogeneous countries that exploit shared fishery resources, and investigate the conditions that lead to a shift from cooperation to competition. We assume that countries differ in their time preferences, initially behave as if the coalition will last indefinitely, use fixed sharing rules during cooperation, and adopt Markovian strategies after withdrawal. Our findings reveal that, for any sharing rule, coalitions of heterogeneous players always break down in finite time. We use the dynamic Shapley Value to decompose the coalition’s aggregate worth over time, thereby eliminating the incentive to leave the agreement. Additionally, we show that a fishing moratorium policy accelerates the recovery of near-extinct fish stocks; however, fishing should resume under a cooperative regime once sustainable levels are achieved.