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

The Secondary Spectrum Market 1 We require an auction protocol for secondary spectrum access that is Revenue-Maximizing Strategyproof (truthful) Interference-free Efficiently Computable We require an auction protocol for secondary spectrum access that is Revenue-Maximizing Strategyproof (truthful) Interference-free Efficiently Computable

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 , 2003]  Existing allocated spectrum is badly utilized!  Solution: Secondary spectrum access  Allow secondary users to utilize idle spectrum 2

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 3

Dynamic Spectrum Allocation - Challenges  Allocation  How do we allocate spectrum?  Avoid interference  Exploit spatial reusability  Payment  How much should secondary users be charged? 4 “Who gets the spectrum, and at what price?” Auctions!

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 5 Achieving all four properties simultaneously is non-trivial

Example - Interference-Free Assignment Interference { CH1, CH2 } Channels CH1 CH2

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 7 Achieving all four properties simultaneously is non-trivial

Best known truthful auction in economics 8  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

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 9 Must resort to approximation algorithms and suboptimal allocation

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 10 We can no longer rely on the VCG mechanism

Solution? 11  Forget about VCG - design auction from scratch  How do we get a truthful auction?  Examine characterization of truthfulness in an auction

Mathematical description of auctions 12  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

Characterizing truthfulness If an agent wins the auction, charge her the minimum bid that guarantees winning Charge winning agents a bid independent price 13

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 14

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? 15

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 16

The random sampling auction 1. Randomly assign bidders to one of two sets, A and B  Flip a coin for each agent. Heads => A, Tails => B 2. Compute optimal revenue for A, $A 3. Compute optimal revenue for B, $B 4. Attempt to “extract” $A from bidders in B 5. Attempt to “extract” $B from bidders in A 17 [Fiat et al., ACM STOC 2002] [Goldberg et al., Games and Economic Behavior, 2006] [Fiat et al., ACM STOC 2002] [Goldberg et al., Games and Economic Behavior, 2006]

Random sampling auction - Analysis 18  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

An idea for reduction 19  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?

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 20

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 21

Conclusion 22  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?