Revenue-Optimal Mechanism Design for Rate-Differentiated Energy Services

The problem of designing revenue-optimal mechanisms for allocating multiple units of a good to consumers over T time steps is considered. Each consumer wants to receive E units of the good and has a delivery rate constraint that limits the number of units it can receive within one time step. Each consumer's rate constraint and valuation for the goods are its private information. Resource allocation problems of this type arise in the context of energy services where consumers have a tolerable rate of energy delivery that cannot be exceeded when they receive their demanded energy. We characterize the allocation rule for a Bayesian incentive compatible, individually rational and revenue maximizing mechanism in terms of solutions to integer programs. The corresponding payment rule is also pinned down by the allocation rule in the form of an integral equation. We then reformulate the problem of finding optimal allocations as a network flow optimization problem. A complete characterization of the optimal allocations and payments is then provided in terms of the solution to the corresponding network flow optimization problem which can be obtained efficiently using the methods developed in the context of discrete optimization [1], [2]. A numerical example is provided to verify our results.