On the efficiency of sequential auctions for spectrum sharing

  • Authors:

  • Junjik Bae;Eyal Beigman;Randall Berry;Michael L. Honig;Rakesh Vohra

  • Affiliations:

  • Boston consulting Group, Seoul, Korea;Olin Business School, Washington University, St. Louis;Department of Electrical Engineering and Computer Science at Northwestern University;Department of Electrical Engineering and Computer Science at Northwestern University;CMS-EMS, Kellogg School of Management at Northwestern University

  • Venue:
  • GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

Abstract

In previous work we have studied the use of sequential second price auctions for sharing a wireless resource, such as bandwidth or power. The resource is assumed to be managed by a spectrum broker (auctioneer), who collects bids and allocates discrete units of the resource. It is well known that a second price auction for a single indivisible good has an efficient dominant strategy equilibrium; this is no longer the case when multiple units of a homogeneous good are sold in repeated iterations. Previous work attempted to bound this inefficiency loss for two users with nonincreasing marginal valuations and full information. This work was based on studying a setting in which one agent's valuation for each resource unit is strictly larger than any of the other agent's valuations and assuming a certain property of the price paid by such a dominant user in any sub-game. Using this assumption it was shown that the worst-case efficiency loss was no more than e-1. However, here we show that this assumption is not satisfied for all non-increasing marginals with this dominance property. In spite of this, we show that it is always true for the worst-case marginals for any number of goods and so the worst-case efficiency loss for any non-increasing marginal valuations is still bounded by e-1.