A Prior-Free Revenue Maximizing Auction for Secondary Spectrum Access

1. A Prior-Free Revenue Maximizing Auction for Secondary Spectrum Access Ajay Gopinathan and Zongpeng Li IEEE INFOCOM 2011, Shanghai, China

2. The Secondary Spectrum Market • We require an auction protocol for secondary spectrum access that is • Revenue-Maximizing • Strategyproof (truthful) • Interference-free • Efficiently Computable

3. The myth of spectrum scarcity • Growing number of wirelessly equipped devices • Demand for usable spectrum is increasing • Limited available spectrum • How scarce is spectrum? • Utilization varies over time and space • 15%-85% variation in spectrum utilization [FCC, ET Docket No 03-222, 2003] • Existing allocated spectrum is badly utilized! • Solution: Secondary spectrum access • Allow secondary users to utilize idle spectrum

4. Dynamic Spectrum Allocation • Secondary Spectrum Market • Primary users (AT&T, Verizon etc) • Secondary users (smaller ISPs) • Secondary users lease spectrum from the primary user • Idle spectrum divided into channels • Secondary users pay for obtaining a channel

5. Dynamic Spectrum Allocation - Challenges • Allocation • How do we allocate spectrum? • Avoid interference • Exploit spatial reusability • Payment • How much should secondary users be charged? “Who gets the spectrum, and at what price?” Auctions!

6. Auction Desiderata • Maximize Revenue • Primary user has incentive to lease spectrum • Strategyproof (truthful) • Secondary users have no incentive to lie about valuation • Interference-free allocation • Limited number of channels to be assigned • Channel assignment = Graph colouring (NP-Hard!) • Computationally efficient • Protocol runs in polynomial time Achieving all four properties simultaneously is non-trivial

7. Example - Interference-Free Assignment { CH1, CH2 } Channels Interference CH1 3 CH1 CH2 1 2 4

8. Auction Desiderata • Maximize Revenue • Primary user has incentive to lease spectrum • Strategyproof (truthful) • Secondary users have no incentive to lie about valuation • Interference-free allocation • Limited number of channels to be assigned • Channel assignment = Graph colouring (NP-Hard!) • Computationally efficient • Protocol runs in polynomial time Achieving all four properties simultaneously is non-trivial

9. Best known truthful auction in economics • Vickrey-Clarke-Groves (VCG) mechanism • Family of auction type mechanisms • Best known, widely used mechanism in economics • Versatile and provably strategyproof • Main drawback • Requires access to the optimal allocation • Loses strategyproof property otherwise

10. Auction Desiderata • Maximize Revenue • Primary user has incentive to lease spectrum • Strategyproof (truthful) • Secondary users have no incentive to lie about valuation • Interference-free allocation • Limited number of channels to be assigned • Channel assignment = Graph colouring (NP-Hard!) • Computationally efficient • Protocol runs in polynomial time Must resort to approximation algorithms and suboptimal allocation

11. Auction Desiderata • Maximize Revenue • Primary user has incentive to lease spectrum • Strategyproof (truthful) • Secondary users have no incentive to lie about valuation • Interference-free allocation • Limited number of channels to be assigned • Channel assignment = Graph colouring (NP-Hard!) • Computationally efficient • Protocol runs in polynomial time We can no longer rely on the VCG mechanism

12. Solution? • Forget about VCG - design auction from scratch • How do we get a truthful auction? • Examine characterization of truthfulness in an auction

13. Mathematical description of auctions • Auctions can specified as function of bids • Allocation function • Probability of winning as a function of the bid • Payment rule • Bidders have private valuation • “How much is a channel worth to me?” • Bidders want to maximize

14. Characterizing truthfulness If an agent wins the auction, charge her the minimum bid that guarantees winning Charge winning agents a bid independent price

15. Auction Desiderata • Maximize Revenue • Primary user has incentive to lease spectrum • Strategyproof (truthful) • Secondary users have no incentive to lie about valuation • Interference-free allocation • Limited number of channels to be assigned • Channel assignment = Graph colouring (NP-Hard!) • Computationally efficient • Protocol runs in polynomial time

16. What about revenue? • Vickrey-type auctions have bad revenue properties • E.g. 2 bids of $x > 0 and $0 has no revenue • Solution: reserve price $R • Add imaginary bidder with bid $R • Run Vickrey auction on set of bids • Vickrey auction with reserve prices are optimal • How to compute the optimal $R? • Need prior knowledge of probability distribution of bids What if prior knowledge is unavailable?

17. The prior-free setting • Assume no knowledge of agent valuations • Worse-case setting • Online optimization problem • First studied by Fiat et al. • [Fiat et al., ACM STOC 2002] • Random Sampling Auction • Context of selling digital goods – unlimited supply of items • Key idea: acquire knowledge by sampling bids

18. The random sampling auction • Randomly assign bidders to one of two sets, A and B • Flip a coin for each agent. Heads => A, Tails => B • Compute optimal revenue for A, $A • Compute optimal revenue for B, $B • Attempt to “extract” $A from bidders in B • Attempt to “extract” $B from bidders in A [Fiat et al., ACM STOC 2002] [Goldberg et al., Games and Economic Behavior, 2006]

19. Random sampling auction - Analysis • Equivalent to Vickrey auction with 2 bidders • Each set is a “bidder” • Guarantees minimum of ($A, $B) • Offer price is bid independent – truthful! • 4-approximate revenue guarantee – constant! • Assumes unlimited supply of item being auctioned

20. An idea for reduction • Step 1: Compute a feasible, interference-free channel assignment • Step 2 : All bidders that can be feasibly assigned spectrum participate in the Random Sampling Auction • “Unlimited supply” of channels • Challenges • What is the best type of assignment in Step 1? • Maximize potential revenue in Step 2 • How do we make Step 1 truthful? • Still need to use suboptimal assignment • Can we make the Random Sampling Auction better?

21. Our Contributions • A two-phase auction protocol for maximizing revenue • Phase 1: Truthful and interference-free channel allocation • Highest potential revenue • Works with any MAX-K-CIS approximation algorithm • Tailored payment scheme to ensure truthfulness • Phase 2: Iterative Random Partitioning Auction • Based on the random sampling auction • Only bidders allocated in phase 1 participate (unlimited supply of channels) • Achieves a 3-approximate revenue guarantee

22. Iterative Partitioning Auction • Improving random sampling auction – “Rinse and repeat!” • Choose the set that loses the auction, repeat sampling auction • Participation in future round is bid independent – still truthful! • Analysis is difficult • Revenue in each round is a random variable • Number of rounds is a random variable • Solution: Don’t sample, partition set instead • Revenue is still random variable • Number of rounds is fixed at log n This achieves asymptotically a 3-approximate revenue guarantee

23. Conclusion • We design 2-phase auction protocol for secondary spectrum access • Phase 1: Compute interference-free assignment • Phase 2: Maximize revenue from bidders assigned in Phase 1 • Our two main tools • Myerson’s characterization of truthful mechanisms • Randomization Questions?