In Central Asia, community water governance institutions emerged and prevailed for a long time. By employing an analytical modelling approach using variants of the evolutionary Hawk-Dove game, we scrutinise three epochs' (pre-Tsarist, Tsarist and Soviet) coordination mechanisms and qualitatively compare them in the efficiency spectrum. We find that the pre-Tsarist community water governance setting, due to its synergetic and pluralistic aspects, was associated with higher efficiency than the Tsarist and Soviet periods' settings. The pre-Tsarist community arrangement linked irrigation duties with benefits. Our analytical model reveals how the Tsarist Russian regulation that replaced the election-sanctioning element with a de-facto system appointing the irrigation staff and paying them fixed wages corrupted the well-established pre-Tsarist decentralised water governance. We term this move the "Kaufman drift". Resulting inadequacies in the water governance could have been averted either by restoring the community mechanism's election-sanctioning attribute or else with an alternative approach such as privatising water resources. With the use of the "Krivoshein game," we produce an alternative scenario for the region where we envisage the potential consequences of the water privatisation. Modelling history might not disentangle the complex nature of water governance evolution fully, however, the heuristics we use in the analysis assist in guiding the diagnosis of the matter and its solution. This makes our study well-timed for contemporary Central Asia. The analyses assess current water management's chances to return to ancient principles of election-sanctioning and perspectives of private irrigation water rights.