Multiple equilibria in symmetric strategies for simultaneous auctions in next-generation bandwidth markets

Abstract

We investigate equilibrium properties of a bidding strategy in a situation in which bidders attempt to purchase a given amount of a divisible resource by bidding on multiple auctions. Each seller uses the Progressive Second-Price auction. A domain of application is the next-generation of wireless networks, in which multiple, competing network providers sell bandwidth to multiple users able to aggregate their purchased bandwidth shares. Every bidder needs to coordinate his bids to maximise the utility derived from all auction. In order to deal with aggregation and coordination of bids, we introduce the notion of an aggregate market, which is an artificial construct that each bidder uses to distribute his demand among the auctions. Furthermore, the aggregate market helps to understand convergence of the bidding process occurring at each individual auction. We show that by using an incentive-compatible, efficient mechanism at each single auction bidders have incentives to truthfully reveal their demand to the aggregate market.