Private Capacities in Mechanism Design

Algorithmic mechanism design considers distributed settings where the participants, termed agents, cannot be assumed to follow the protocol but rather their own interests. The protocol can be regarded as an algorithm augmented with a suitable payment rule and the desired condition is termed truthfulness, meaning that it is never convenient for an agent to report false information. Motivated by the applications, we extend the usual one-parameter and multiparameter settings by considering agents with private capacities: each agent can misreport her cost for “executing” a single unit of work and the maximum amount of work that each agent can actually execute (i.e., the capacity of the agent). We show that truthfulness in this setting is equivalent to a simple condition on the underlying algorithm. By applying this result to various problems considered in the literature (e.g., makespan minimization on related machines) we show that only some of the existing approaches to the case “without capacities” can be adapted to the case with private capacities. This poses new interesting algorithmic challenges.