Vickrey Pricing in Network Routing Fast Payment Computation

Eliciting truthful responses from self interested agents is an important problem in game theory and microeconomics and it is studied under mechanism design or implementation theory Truthful mechanisms have received considerable interest within computer science recently for designing protocols for Internet based applications which typically involve cooperation of multiple self interested agents A cornerstone of the mechanism design eld is the Vickrey mechanism or more generally the class of Vickrey Clarke Groves mechanisms These mechanisms are known to be incentive compatible meaning that rational agents maximize their utility by truthfully revealing their preferences In the Vickrey Clarke Groves VCG mechanism each agent receives a payment for his participation and this payment is proportional to the added value he brings to the system Implementing the VCG mechanism often requires solving a non trivial optimization problem n times once with all agents and once corresponding to each agent s deletion to determine his incremental value An important algorithmic challenge is to reduce this computational overhead We investigate this problem in the speci c context of network routing where there has been a surge of interest in pricing network usage Routing in the Internet involves multiple agents such as organizations or service providers who are self interested and thus the Vickrey compensation mechanism is relevant for eliciting truthful response In this context of shortest path routing we show that the Vickrey payments for all the agents can be computed in the same asymptotic time complexity as for one agent thus solving an open problem of Nisan and Ronen