This article introduces evolutionary game theory as an approach to stylised long-term analysis of water governance transformations in Central Asia. This world region has been strongly affected by natural hazards, political disruptions and historically diverse attempts to establish effective water management principles. Drawing on historical and contemporary evidence, we establish a game theoretical baseline model of a user community in which irrigation is efficiently governed by group sanctions. By allowing for drift in the evolutionary equilibrium, we model how a loss of traditional authorities over water management can erode established group norms. We then analyse a hypothetical scenario of privatised water rights, inspired by historical and current policy debates in Central Asia. Under the assumption that such rights can be technically implemented, we show that they can restore an efficient water use equilibrium of owners that is egalitarian and evolutionary stable. We discuss how future climate change scenarios or conflicts over transboundary water allocation may affect the model results, focusing on the effects of increased uncertainty and of decreasing water productivity on system resilience. Productivity shocks may make low-performing equilibria unsustainable and thus lead to disruptive change or extinction of certain equilibria. Policy should focus on local interaction as an arena of institutional change. We suggest empirical research questions emerging from our analysis and highlight the benefits of uncontested property rights as an institutional solution to water governance.