Multi-bid auctions for bandwidth allocation in communication networks

Abstract

Abstract-In this paper, we design a bandwidth pricing mechanism that solves congestion problems in communication networks. The scheme is based on second-price auctions, which are known to be incentive compatible when a single indivisible item is to be sold (users have no interest to lie about the price they are willing to pay for the resource) and to lead to an efficient allocation of resources in the sense that it maximizes social welfare. We prove these properties when an infinitely divisible resource (bandwidth on a communication link) is to be shared among users who are allowed to submit several bids when they want to establish a connection. Our scheme is highly related to the Progressive Second Price Auction of Lazar and Semret where players bid sequentially until an (optimal) equilibrium is reached. While keeping their incentive compatibility and efficiency properties, our scheme presents the advantage that the multi-bid is submitted once only, saving a lot of signalization overhead.

Multi-bid Versus Progressive Second Price Auctions in a Stochastic Environment

“…4 Multi-Bid Auction [9] In the multi-bid scheme, users, when they enter the game, submit a set of M 2-dimensional bids…”

“…As for PSP, incentive compatibility (each user i should better reveal its bandwidth valuation, i.e., p m i = θ ′ ti (q m i ) ∀m), and efficiency are proved, but up to a controlled constant here (see [9] for details).…”

“…It is shown in [9] that it is in the players' interest to submit a uniform quantile repartition of their bids, i.e., (…”

“…Figure 3 illustrates the evolution of the mean efficiency ratio (obtained steadystate social welfare divided by the optimal one), the mean network revenue and the complexity of the algorithm when the number M of multiple bids increases, and compares those performance measures with the ones obtained for PSP. The complexity of computing PSP allocations and prices is of the order O(I 2 ) [11], and the complexity of multi-bid auction is of the order O(M × I 2 ) [9]. We therefore display the mean number of applications of each auction rule by unit of time, multiplying this number by M for multi-bid auction.…”

“…In [9], multi-bid auction (a one-shot version of PSP) has been proposed. It consists for each player in submitting multiple bids once only, providing therefore an approximation of her own valuation function.…”