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

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 2

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] 3 [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).

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 4

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 5

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 6

Challenges of Double Spectrum Auction Design Some truthful auction designs 7 [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).

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 8

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 9

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 10

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

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: 12

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

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 14

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 15

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 16

Experimental Results － Simulation Setup Allocation algorithm ◦ Max-IS [21] ◦ Greedy-U [17] ◦ Greedy [17] ◦ RAND Interference condition ◦ Random ◦ Clustered 17 [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).

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

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

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