This paper analyzes a game theoretic model of groundwater extraction in an asymmetric two-cell aquifer under incomplete information about the extent to which the local stock of groundwater depends on the extraction histories at nearby wells. A novel assumption is that the elevation of the bottom of the aquifer differs across, otherwise identical, cells. Asymmetry creates a strategic advantage (disadvantage) for the user in the deep (shallow) cell in “stealing” neighbor’s water. The user with a larger initial stock actually benefits from the commonality of groundwater provided that the asymmetry is not too small or too great. Assuming that the asymmetry between users is sufficiently large, better informed, non-cooperative users attain a higher joint welfare when the prior belief about the rate of transmission is sufficiently dispersed. Moreover, better hydrologic information may allow non-cooperative users to achieve maximum social welfare even in the absence of groundwater use regulations. Yet, in an asymmetric aquifer there may be both winners and losers from better public information.