Mechanisms for Efficient Allocation in Divisible Capacity Networks

We propose a mechanism for auctioning bundles of multiple divisible goods. Such a mechanism is very useful for allocation of bandwidth in a network where the buyers want the same amount of bandwidth on each link in their route. We first propose a single-sided VCG-type mechanism. However, instead of reporting types, the players only reveal a two-dimensional bid signal - the maximum quantity that they want and the per unit price they are willing to pay. We show the existence of an efficient Nash equilibrium in the corresponding auction game of the mechanism. We show through an example that not all Nash equilibria are efficient but provide a distributed algorithm that yields the efficient one. Further, we provide a sufficient characterization of all efficient Nash equilibria. We then present a double-sided auction mechanism for multiple divisible goods, and show that there exists a Nash equilibrium of the auction game which yields the efficient allocation