Abstract
We study a sequential auction for sharing a wireless resource (bandwidth or power) among competing transmitters. The resource is assumed to be managed by a spectrum broker (auctioneer), who collects bids and allocates discrete units of the resource via a sequential second-price auction. 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. For two users with full information, we show that such an auction has a unique equilibrium allocation. The worst-case efficiency of this allocation is characterized under the following cases: (i) both bidders have a concave valuation for the spectrum resource, and (ii) one bidder has a concave valuation and the other bidder has a convex valuation (e.g., for the other user's power). Although the worst-case efficiency loss can be significant, numerical results are presented, which show that for randomly placed transmitter-receiver pairs with rate utility functions, the sequential second-price auction typically achieves the efficient allocation. For more than two users it is shown that this mechanism always has a pure strategy equilibrium, but in general there may be multiple equilibria. We give a constructive procedure for finding one equilibrium; numerical results show that when all users have concave valuations the efficiency loss decreases with an increase in the number of users.
Original language | English (US) |
---|---|
Article number | 4604744 |
Pages (from-to) | 1193-1203 |
Number of pages | 11 |
Journal | IEEE Journal on Selected Areas in Communications |
Volume | 26 |
Issue number | 7 |
DOIs | |
State | Published - Sep 2008 |
Funding
Manuscript received August 15, 2007; revised March 10, 2008. This research was supported in part by NSF under grant CNS-0519935. This work was presented in part at the Second International Conference on Cognitive Radio Oriented Wireless Networks and Communications in Orlando, Florida, USA, and the 46th IEEE Conference on Decision and Control in New Orleans, LA, USA.
Keywords
- Auction
- Dynamic spectrum sharing
- Efficiency
- Equilibrium
- Mechanism design
- Resource allocation
ASJC Scopus subject areas
- Computer Networks and Communications
- Electrical and Electronic Engineering