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!