In this paper, we introduce a game theoretic model of groundwater extraction in a two-cell aquifer under incomplete information. A novel assumption is that individual users have incomplete knowledge of the speed of lateral flows in the aquifer: although a user is aware that his neighbor's water use has some influence on their future water stock, they are uncertain about the degree of this impact. We find that the lack of information may either increase or decrease the rate of water use and welfare. In a two-period framework, the relevant characteristic is the ratio of the periodic marginal benefits of water use. Depending on whether this ratio is convex or concave, the average speed with which the aquifer is depleted decreases or increases when users learn more about the local hydrologic properties of groundwater. We also show that the effect of better information on the welfare of the average producer may be negative even in the situations when, on average, groundwater is allocated more efficiently across irrigation seasons.