  Consider a group of effort-averse, or lazy, sensors that seek to minimize the
effort invested to collect measurements of a variable. Increasing the effort
invested by the sensors improves the quality of the measurements provided to
the central planner but this incurs increased costs to the sensors. The central
planner, which processes the sensor measurements, employs an averaging
estimator. It also determines contracts for rewarding sensors based on the
measurements obtained. The problem of designing a contract that yields an
estimation-error based quality-of-service level in return for the reward
extended to sensors is investigated in this paper. To this end, a game is
formulated between the central planner and the sensors. Conditions for the
existence and uniqueness of an equilibrium are identified. The equilibrium is
constructed explicitly and its properties in response to a reward based
contract are studied. It turns out that the central planner, while not being
able to directly measure the effort invested by the sensors, can enhance the
estimation quality by rewarding each sensor based on the distance of its
measurements from the output of the averaging estimator. Ultimately, optimal
contracts are designed from the perspective of the budget required for
achieving a specified level of estimation error.
