Abstract <p>The imbalance between the supply and demand of global water resources is intensifying the competition between riparian countries for water resources in transboundary river basins. Recognizing that the sizes of riparian country coalitions are finite is a fundamental prerequisite for understanding the strategic choices and evolutionary mechanisms of water resources cooperation. This study develops a bimatrix stochastic evolutionary game model to analyze water resources cooperation among finite-sized riparian country coalitions, using the selection-mutation Moran process. By calculating equilibrium frequencies of different strategies under stochastic perturbations and conducting numerical simulations, the driving factors and mechanisms underlying the dominance of cooperative strategies are explored. The results indicate that lower strategy mutation rates enhance cooperation between upstream and downstream coalitions. The incentive and constraint mechanisms strengthen cooperative tendencies. And the effect of coalition size is dual: when incentives and constraints are present, larger coalitions facilitate the evolution of cooperative strategies; otherwise, they undermine the prospects for cooperation. Moreover, the composition of the two-game coalitions (featuring small upstream countries and relatively large downstream countries) creates opportunities for cooperation even in the absence of formal mechanisms. Designing effective incentive and constraint mechanisms is essential for shifting away from the narrow zero-sum mindset and reshaping cooperation preferences, particularly among large-scale coalitions of riparian countries operating under stochastic perturbations.</p> Graphical Abstract <p></p>