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Consider a group of effort-averse, or lazy, sensors that seek to minimize theeffort invested to collect measurements of a variable. Increasing the effortinvested by the sensors improves the quality of the measurements provided tothe central planner but this incurs increased costs to the sensors. The centralplanner, which processes the sensor measurements, employs an averagingestimator. It also determines contracts for rewarding sensors based on themeasurements obtained. The problem of designing a contract that yields anestimation-error based quality-of-service level in return for the rewardextended to sensors is investigated in this paper. To this end, a game isformulated between the central planner and the sensors. Conditions for theexistence and uniqueness of an equilibrium are identified. The equilibrium isconstructed explicitly and its properties in response to a reward basedcontract are studied. It turns out that the central planner, while not beingable to directly measure the effort invested by the sensors, can enhance theestimation quality by rewarding each sensor based on the distance of itsmeasurements from the output of the averaging estimator. Ultimately, optimalcontracts are designed from the perspective of the budget required forachieving a specified level of estimation error.

Budget-Constrained Contract Design for Effort-Averse Sensors in Averaging Based Estimation