A central planner wishes to engage a collection of sensors to measure a quantity. Each sensor seeks to trade-off the effort it invests to obtain and report a measurement, against contracted reward. Assuming that measurement quality improves as a sensor increases the effort it invests, the problem of the reward contract design is investigated. To this end, a game is formulated between the central planner and the sensors. Using this game, it is established that the central planner can enhance the quality of the estimate by rewarding each sensor based on the distance between the average of the received measurements and the measurement provided by the sensor. Optimal contracts are designed from the perspective of the budget required to achieve a specified level of error performance.