Strategyproof Auctions For Balancing Social Welfare and Fairness in Secondary Spectrum Markets Ajay Gopinathan, Zongpeng Li University of Calgary Chuan Wu University of Hong Kong INFOCOM 2011, Shanghai, China

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

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

The Secondary Spectrum Market

Properties of secondary spectrum auctions  Unique spatial property  Channels can be reused  Interference-free assignment  Unique temporal property  Auctions are repeated!  Leads to more efficient utilization of spectrum  Previous work tend to only focus on spatial aspect

Previous Work  Maximize social welfare  [Zhou et al., ACM MOBICOM 2008]  [Wu et al., IEEE Trans. On Communications 2009]  Maximize revenue  [Jia et al, ACM MOBIHOC 2009]  [Gopinathan and Li, IEEE INFOCOM 2011]  Previous work only consider the spatial property  Design of strategyproof auctions for use with poly-time suboptimal channel assignment

Our focus  Not only on social welfare maximization in individual auctions, but also on fairness to each secondary user  To guarantee each user gets a channel from time to time  Three questions:  How serious is unfairness in spectrum auctions?  Why do we need to guarantee fairness in secondary spectrum markets?  How do we guarantee fairness in secondary spectrum markets?

How serious is unfairness: an example 1 1 Interference { CH1 } Channels

How serious is unfairness: an example 1 1 Interference { CH1 } Channels

How serious is unfairness: an example 1 1 Interference { CH1 } Channels Social Welfare Maximizing Channel Assignment

How serious is unfairness: an example 1 1 Interference { CH1 } Channels CH1 Social Welfare Maximizing Channel Assignment

How serious is unfairness: an example 1 1 Interference { CH1 } Channels

How serious is unfairness: an example 1 1 Interference { CH1 } Channels Social Welfare Maximizing Channel Assignment CH1

How serious is unfairness: an example 1 1 Interference { CH1 } Channels Social Welfare Maximizing Channel Assignment CH1 User 1 must value the channel three times as much to be guaranteed a channel!

Why fairness is needed  Increase diversity of users who win  Encourage bidders to continue to participate [1]  Bidders dropping out leads to loss of revenue and reduction of social welfare in the long run!  Discourage vindictive bidding [1][2]  Bidders with no chance to win increase their bids, causing winning users to pay a higher price [1] C. Meek, D. Chickering, D. Wilson, “Stochastic and Contingent Payment Auctions,” in 1 st Workshop on Sponsored Search Auctions, 2005 [2] Y. Zhou, R. Lukose, “Vindictive Bidding in Keyword Auctions,” ICEC, 2007.

How to guarantee fairness  Since auctions are repeated, there is room to introduce fairness  “Local” fairness: as long as a user’s valuation is at least as high as neighbors, it is allocated a channel occasionally  Max-min fairness: each user’s probability of being assigned a channel is at least proportional to its max-min share m(i) in the conflict graph  Computed using a water-filling type approach

Auction Desiderata  Trade-off social welfare maximization with diversity of winning bidders (fairness)  Ideally, allow auctioneer to choose the trade-off amount  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

Auction Desiderata  Trade-off social welfare maximization with diversity of winning bidders  Ideally, allow auctioneer to choose the trade-off amount  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 Rules out VCG auction mechanisms N. Nisan and A. Ronen, “Computationally feasible VCG mechanisms,”Journal of Artificial Intelligence Research, vol. 29, pp. 19–47, 2007.

Achieving “local” fairness  Introduce randomization into the channel assignment  Achieve trade-off between social welfare and fairness in expectation  Fairness achieved in the time domain – suitable for repeated auction setting  Trick is to ensure auction can be made strategyproof even with randomization

Truthful auction characterization

Our solution  Use Myerson’s result to design truthful auction  Step 1: Customize an approximation algorithm for maximizing social welfare with fairness constraints  Randomized assignment to increase user diversity  Monotonically non-decreasing in bids  Step 2: Design payment scheme  Dependent on approximation algorithm used in step 1  => Achieves “local” fairness with strategyproof auctions  Can be used to guarantee a minimum level of allocation to each secondary user in expectation

Achieving global fairness  How can we achieve global measures of fairness?  E.g. assigned a channel proportional to max-min fair share in conflict graph

Achieving global fairness  Assume fractional allocation is allowed, then let be a fractional channel assignment for user that achieves desired trade-off between global fairness and social welfare  Let be set of all feasible channel assignments  Exponentially many!  Basic idea: Decompose into feasible solutions with an associated probability,  Pick some solution with probability  Achieve fairness tradeoff in expectation

The primal LP  Need to compute probabilities  Solution uses the following linear program  Problem - Exponential number of variables in this LP!

The dual LP  Solution is to use the dual:  Exponential constraints, but can use ellipsoid method with suitable separation oracle for poly-time computation

Conclusion  Secondary spectrum auctions promising approach to mitigate spectrum scarcity problem  Previous work consider only spatial characteristic of such auction, ignore temporal aspect  In repeated auction, increasing user diversity  encourages user participation  discourages vindictive bidding  Our contribution  Truthful auction framework for balancing social welfare and fairness  Both global and local fairness solutions provided

Thank you!