Competition arises from the cooperative or non-cooperative exploitation of an aquifer by all those with a right to its ground water. It is shown that the competition for a shared ground-water can be framed as a problem of game theory whose outcome depends on whether or not there is cooperation among ground-water pumpers. There is a second important element that plays out in the management of ground water, namely that of uncertainty. That arises from climate variability and possible climate change and their effects on ground water recharge. But population growth and future human pressures for ground water are also uncertain. Thus, a sustainable ground-water management strategy must be searched for in an environment in which bot human and natural are only partly unknown and perhaps adversarial. This paper presents a ground-water management methodology to cope with competition and uncertainty in the quest for sustainable aquifer exploitation. Two examples of regional aquifers illustrate the methodology.