We study water use by two geographically proximate farmers in a particular region during a drought. The two farmers each have an endowment of time that can be used either to produce water or to steal water. The price of water is exogenously given. The goal of the two farmers is to maximize their wealth from water production and water theft. In this setting, we perform three tasks. First, we determine the Nash equilibrium of the game-theoretic interaction between the two farmers. Second, we study how this equilibrium depends on the ease with which water can be stolen. Finally, we show how the preceding equilibrium is impacted when there is no water theft and then we determine the maximum amount that a farmer would be willing to pay to prevent theft.

我们研究了干旱期间特定地区的两个地理位置相近的农民的用水情况。这两个农民各有天资，可以用来生产水或偷水。水的价格是外生给定的。两位农民的目标是从生产水和偷水中获得最大的财富。在此设置中，我们执行三项任务。首先，我们确定两个农民之间博弈论相互作用的纳什均衡。其次，我们研究这种平衡如何取决于偷水的难易程度。最后，我们展示了在没有偷水的情况下之前的均衡是如何受到影响的，然后我们确定农民愿意支付的最大金额来防止偷水。