An Efficient Nash-Implementation Mechanism for Divisible Resource Allocation

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 allow for buyers to specify multiple routes (corresponding to a source-destination pair). The total flow can then be split among these multiple routes. We first propose a single-sided VCG-type mechanism. However, instead of reporting their valuation functions, 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. The proposed mechanism is a weak Nash-implementation, i.e., it has a non-unique Nash equilibrium that implements the social-welfare maximizing allocation. We show the existence of an efficient Nash equilibrium in the corresponding auction game. We show through an example that there are other Nash equilibria that are not efficient. Further, we provide a sufficient characterization of all efficient Nash equilibria. We then generalize this to buyers getting arbitrary amounts of various goods. This require each buyer to submit a bid separately for each good but their utility function a general function of allocations of various divisible goods. Then, we present a doublesided auction mechanism for multiple divisible goods with buyers and sellers. We show that there exists a Nash equilibrium of this auction game which yields the efficient allocation.