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We design an optimal contract between a demand response aggregator (DRA) and power grid customers for incentive-based demand response. We consider a setting in which the customers are asked to reduce their electricity consumption by the DRA and they are compensated for this demand curtailment. However, given that the DRA must supply every customer with as much power as she desires, a strategic customer can temporarily increase her base load in order to report a larger reduction as part of the demand response event. The DRA wishes to incentivize the customers both to make costly effort to reduce load and to not falsify the reported load reduction. We model this problem as a contract design problem and present a solution. The proposed contract consists of two parts: a part that depends on (the possibly inflated) load reduction as measured by the DRA and another that provides a share of the profit that accrues to the DRA through the demand response event to the customers. Since this profit accrues due to the total load reduction because of the actions taken by all the customers, the interaction among the customers also needs to be carefully included in the contract design. The contract design and its properties are presented and illustrated through examples.

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We study a setup in which a system operator hires a sensor to exert costly effort to collect accurate measurements of a value of interest over time. At each time, the sensor is asked to report his observation to the operator, and is compensated based on the accuracy of this observation. Since both the effort and observation are private information for the sensor, a naive payment scheme which compensates the sensor based only on his self-reported values will lead to both shirking and falsification of outcomes by the sensor. We consider the problem of designing an appropriate compensation scheme to incentivize the sensor to at once exert costly effort and truthfully reveal the resulting observation.To this end, we formulate the problem as a repeated game and propose a compensation scheme that employs stochastic verification by the operator coupled with a system of assigning reputation to the sensor. In particular, our proposed payment scheme compensates the sensor based on both the effort in the current period as well as the history of past behavior. We show that by using past behavior in determining present payments, the operator can both incentivize higher effort as well as more frequent truthtelling by the sensor and decrease the required verification frequency.