According to international law, straddling fish stocks should bemanaged cooperatively through regional fisheries management organizations (RFMOs). This paper analyzes the stability and success of these organizations through a game in partition function form based on the classical Gordon-Schaefer bioeconomic model. Results show that the larger the number of fishing states that compete for the fish stock the higher are the relative gains from full cooperation, but the lower is the likelihood of large RFMOs being stable. It is also shown that new entrants increase the incentives of RFMO members to leave and decrease the incentives of non-members to join it. Moreover, the success of coalition formation is positively correlated with the degree of cost asymmetry among fishing states and negatively with the overall level of efficiency.