strategyproof auctions for balancing social welfare and fairness in secondary spectrum markets
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Strategyproof Auctions For Balancing Social Welfare and Fairness in Secondary Spectrum Markets. INFOCOM 2011, Shanghai, China. Ajay Gopinathan, Zongpeng Li University of Calgary. Chuan Wu University of Hong Kong. The myth of spectrum scarcity. - PowerPoint PPT PresentationTRANSCRIPT
Strategyproof Auctions For Balancing Social Welfare and Fairness in Secondary Spectrum
Markets
Ajay Gopinathan, Zongpeng LiUniversity of Calgary
Chuan WuUniversity 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 03-222, 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
Interference
2
3
4
{ CH1 } Channels
How serious is unfairness: an example
1
Interference
2
3
4
{ CH1 } Channels
How serious is unfairness: an example
1
Interference
2
3
4
{ CH1 } ChannelsSocial Welfare MaximizingChannel Assignment
How serious is unfairness: an example
1
Interference
2
3
4
{ CH1 } Channels
CH1
CH1CH1
Social Welfare MaximizingChannel Assignment
How serious is unfairness: an example
1
Interference
2
3
4
{ CH1 } Channels
How serious is unfairness: an example
1
Interference
2
3
4
{ CH1 } ChannelsSocial Welfare MaximizingChannel Assignment
CH1
How serious is unfairness: an example
1
Interference
2
3
4
{ CH1 } ChannelsSocial Welfare MaximizingChannel 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 1st 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 timeAchieving 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 timeRules 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!