TRUST:A General Framework for Truthful Double Spectrum Auctions

1. TRUST:AGeneral Framework for Truthful Double Spectrum Auctions Xia Zhou and Heather Zheng Department of Computer Science, University of California, Santa Barbara, CA 93106 • IEEE INFOCOM (2009)

2. Introduction • Well-designed auctions provide fairness and efficiency • In the past decade, the FCC have been using single-sided auctions to allocate spectrum • In order to improve spectrum utilization, a new spectrum double auction framework is proposed • Exploit spatial reusability

3. Introduction • Reusability makes spectrum different from conventional goods and difficult to design • Conventional auctions do not consider reusability[1][14] • Spectrum auctions only consider single-sided[25] [1] BABAIOFF, M., AND NISAN, N. Concurrent auctions across the supply chain. In Proc. of Economic Commerce (2001). [14] MCAFEE, R. P. A dominant strategy double auction. Journal of Economic Theory 56, 2 (April 1992), 434–450. [25] ZHOU, X., GANDHI, S., SURI, S., AND ZHENG, H. eBay in the sky: Strategy-proof wireless spectrum auctions. In Proc. of MobiCom (Sept. 2008).

4. Introduction • A framework for truthful double spectrum auction(TRUST) is proposed • Integrate spectrum allocation and pricing components to improve spectrum utilization • TRUST can use any spectrum allocation algorithm • TRUST guarantees three economic properties, truthfulness, individual rationality and ex-post budget balance

5. Double Spectrum Auction Problems －Problem Model • The goal is to improve spectrum utilization and to achieve economic properties • Consider single-round double spectrum auction • One auctioneer, M sellers, N buyers • Same time term • Sealed-bid and private

6. Double Spectrum Auction Problems－Required Economic Properties • three critical properties required to design economic-robust double auctions • Truthfulness • No seller m or buyer n can improve its own utility by bidding untruthfully • Individual Rationality • No winning seller is paid less than its bid and no winning buyer pays more than its bid • Ex-Post Budget Balance • The auctioneer’s profit ≧0

7. Challenges of Double Spectrum Auction Design • Some truthful auction designs [1] [14] [25] [1] BABAIOFF, M., AND NISAN, N. Concurrent auctions across the supply chain. In Proc. of Economic Commerce (2001). [14] MCAFEE, R. P. A dominant strategy double auction. Journal of Economic Theory 56, 2 (April 1992), 434–450. [25] ZHOU, X., GANDHI, S., SURI, S., AND ZHENG, H. eBay in the sky: Strategy-proof wireless spectrum auctions. In Proc. of MobiCom (Sept. 2008).

8. Challenges of Double Spectrum Auction Design • McAfee double auction • Sort bids in non-decreasing (for sellers) and non-increasing (for buyers) orders • The first (k − 1) sellers and the first (k − 1) buyers are the auction winners • All winning buyers are charged • All winning sellers are paid

9. TRUST－Design Rationale • It follows McAfee’s design and combines reusability • Map a group of buyers into each seller • In TRUST, form buyer groups based on their interference condition • Uniform pricing within each buyer group • Group bid≦lowest bid*number of buyers

10. TRUST－Design Details • TRUST performs the auction in three steps • Step 1:Buyer group formation • Buyers assigned to the same channel are organized into the same group • Use different spectrum allocation algorithms to cope with various interference models

11. TRUST－Design Details • Step 2:Winner Determination • Each group is a “super buyer” and has a “group bid( )” • Gl: represent one of the groups • nl: number of buyers in the group l • As McAfee, sort the seller bids and group bids and determine k

12. TRUST－Design Details • Step 3:Pricing • As McAfee, each winning seller is paid kth seller’s bid, and each winning group should pay kth group’s bid • The group price is shared among all buyers in the group: • The auctioneer’s profit is:

13. TRUST－an Illustrative Example • OPT : optimal algorithm to minimize the number of channels • RAND : randomly produced allocation result

14. TRUST－Proof of Auction Properties • Ex-post budget balanced • Because k is the largest index satisfies that buyer’s bid ≧seller’s bid • Individual rational • Because the sort, buyers pay less than their bids and sellers get more than their bids

15. TRUST－Proof of Auction Properties • Truthfulness • Lemma 1. if buyer n wins by bidding Bn , then also wins by bidding Bn’> Bn • Lemma 2. if seller m wins by bidding Bm, then also wins by bidding Bm’< Bm • Lemma 3. if buyer n wins by bidding Bn and Bn’, the price Pn charged to n is the same for both • Lemma 4. if seller m wins by bidding Bm and Bm’, then the payment Pm to m is the same for both

16. TRUST－Proof of Auction Properties • Truthfulness (for buyer) • Any buyer n cannot obtain higher utility by bidding Bn’≠Vn • Case1. both get zero utility • Case2. happens if Bn’<Vn. Bn’ bidder gets no utility • Case3. happens if Bn’>Vn. When Bn’ bidder wins, he should pay Vn<p<Bn’ ∴utility<0 • Case4. both get the same utility

17. Experimental Results－ Simulation Setup • Allocation algorithm • Max-IS[21] • Greedy-U[17] • Greedy[17] • RAND • Interference condition • Random • Clustered [17] RAMANATHAN, S. A unified framework and algorithm for channel assignment in wireless networks. Wirel. Netw. 5, 2 (1999), 81–94. [21] SUBRAMANIAN, A. P., GUPTA, H., DAS, S. R., AND BUDDHIKOT, M. M. Fast spectrum allocation in coordinated dynamic spectrum access based cellular networks. In Proc. of IEEE DySPAN (November 2007).

18. Experimental Results－Economic Impact on Spectrum Distribution • Compare TRUST to PA(Pure Allocation) • Causes: choice of winning groups

19. Experimental Results－Choosing Allocation Algorithm in TRUST • An effective allocation is important to TRUST • Limit the size of each group

20. Conclusion • TRUST achieves truthfulness, individual nationality and ex-post budget balance, and enable spectrum reuse • Tradeoff between spectrum efficiency and economic robustness