Truthful Spectrum Auction Truthful Spectrum Auction Design for Secondary Design for Secondary Networks Networks Yuefei Zhu Yuefei Zhu ∗ ∗ , Baochun Li , Baochun Li ∗ ∗ and Zongpeng and Zongpeng Li Li † † ∗ ∗ Electrical and Computer Engineering, University of Electrical and Computer Engineering, University of Toronto Toronto † Computer Science, University of Calgary Computer Science, University of Calgary
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Truthful Spectrum Auction Design for Secondary Networks Yuefei Zhu ∗, Baochun Li ∗ and Zongpeng Li † ∗ Electrical and Computer Engineering, University.
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Truthful Spectrum Auction Truthful Spectrum Auction Design for Secondary Design for Secondary
NetworksNetworks
Yuefei ZhuYuefei Zhu∗∗, Baochun Li, Baochun Li∗∗ and Zongpeng Li and Zongpeng Li††
∗ ∗ Electrical and Computer Engineering, University of TorontoElectrical and Computer Engineering, University of Toronto†† Computer Science, University of CalgaryComputer Science, University of Calgary
Spectrum scarcitySpectrum scarcity
There is a There is a spectrum shortagespectrum shortage
AT&T: U.S. is quickly running out of AT&T: U.S. is quickly running out of spectrum (February 2012)spectrum (February 2012)
Solutions such as secondary access Solutions such as secondary access mitigate the problemmitigate the problem
GreedilyGreedily assignassign channels to channels to shortest paths as long as there are shortest paths as long as there are channels feasible for assignmentchannels feasible for assignment
•
InterferencInterference e consideredconsidered
Our idea: PaymentOur idea: PaymentGet a winner Get a winner ii ’’s s ““critical bidcritical bid””::
Set Set bbii to 0, run the greedy assignment. to 0, run the greedy assignment. The first bidder that makes it infeasible The first bidder that makes it infeasible to accommodate to accommodate i i along its path is along its path is ii ’’s s ““critical biddercritical bidder””. .
This This ““critical biddercritical bidder”” submits a submits a ““critical critical bidbid”” of of ii
PaymentPayment: :
Payment:Payment:
A toy exampleA toy example
TruthfulnessTruthfulnessLemma: The heuristic auction is individually rational.
is always no larger than
Theorem: The heuristic auction is truthful.
Proof of truthfulness is based on:
1.monotonic winner determination
2.bid-independent pricing
• (Myerson’s characterization (1981))
A randomized auctionA randomized auction
Problem formulationProblem formulationAn integer program:An integer program:
• Winner determination to weighted Winner determination to weighted max-flowmax-flow
Social Social welfarewelfare
s.t.s.t.
DecompositionDecompositionRelaxRelax the variables to the variables to [0,1][0,1], getting , getting a linear program (LPR)a linear program (LPR)
If the integrality gap between the If the integrality gap between the integer program (IP) and the LPR is integer program (IP) and the LPR is at most , we can at most , we can decomposedecompose the optimal solution asthe optimal solution as
feasible feasible assignmeassignmentnt
Decomposition (contDecomposition (cont’’d)d)
, we can view , we can view this decomposition as this decomposition as a probability a probability distributiondistribution over the integer over the integer solutions, where a feasible channel solutions, where a feasible channel assignment is selected with assignment is selected with probability probability
PaymentPaymentA A VCG-likeVCG-like payment is used for payment is used for ensuring truthfulness (in ensuring truthfulness (in expectation) and approximately expectation) and approximately maximizing social welfare: maximizing social welfare:
ResultsResultsTheorem: Theorem: The randomized auction The randomized auction is truthful in expectation.is truthful in expectation.
Theorem: Theorem: The randomized auction The randomized auction achieves optimal social welfare achieves optimal social welfare in expectation.in expectation.
Simulation resultsSimulation results
Auction efficiency with Auction efficiency with different numbers of SNs different numbers of SNs
enrolledenrolled
Auction efficiency with Auction efficiency with different sizes of SNsdifferent sizes of SNs
Auction efficiency with Auction efficiency with different auction settingsdifferent auction settings