Efficiency Bounds for Sequential Wireless Resource Allocation Auctions

A sequential auction mechanism is proposed 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 sequentially discrete units of the resource via second-price auctions. It is known that such auctions can have inefficient equilibria. For two users with full information, this mechanism is shown to give a unique allocation. The worst-case efficiency of this allocation is characterized under the following cases: (i) both bidders have a concave valuation of 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 transmitterreceiver pairs with rate utility functions, the sequential secondprice auction typically achieves the efficient allocation. For more than two users it is shown that this mechanism 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 than when all users have concave valuation the efficiency loss decreases when the number of users increases.