Achieving an efficient equilibrium when simultaneously bidding on multiple, divisible-item auctions

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. A possible application area for such a scenario is the next-generation of wireless networks, in which multiple, competing network providers sell bandwidth each using an auction to allocate their resources. A bidder may aggregate shares of the resource obtained from some of the auctions, and needs to coordinate his bids to maximise the utility derived from each auction. In order to deal with aggregation and coordination of bids, we introduce the notion of an aggregated market, which is an artificial construct by each bidder that allows him 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 aggregated market.