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Truthful Spectrum Auction Design for Secondary Networks Yuefei Zhu ∗, Baochun Li ∗ and Zongpeng Li † ∗ Electrical and Computer Engineering, University of Toronto † Computer Science, University of Calgary

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Spectrum scarcity There is a spectrum shortage AT&T: U.S. is quickly running out of spectrum (February 2012) Solutions such as secondary access mitigate the problem Secondary spectrum auctions

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Need for multi-hop support ╳

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Multi-hop transmission

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What are the difficulties for multi-hop supported auctions?

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Challenges Unawareness: unknown of the # of channels to bid for. Interference: more complicated Truthfulness: desirable but difficult to achieve

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Contributions A heuristic auction guarantees truthfulness provides winning SNs with interference-free end-to-end multi-hop paths A randomized auction truthful in expectation provably approximately-optimal in social welfare

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A heuristic truthful auction

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Our idea: Channel assignment Virtual bid for SN i: Sort SNs: Greedily assign channels to shortest paths as long as there are channels feasible for assignment Interference considered

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Our idea: Payment Get a winner i’s “critical bid”: Set b i to 0, run the greedy assignment. The first bidder that makes it infeasible to accommodate i along its path is i’s “critical bidder”. This “critical bidder” submits a “critical bid” of i Payment:

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Payment: A toy example

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Truthfulness Lemma: The heuristic auction is individually rational. is always no larger than Theorem: The heuristic auction is truthful. Proof of truthfulness is based on: monotonic winner determination bid-independent pricing (Myerson’s characterization (1981))

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A randomized auction

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Problem formulation An integer program: Winner determination to weighted max- flow Winner determination to weighted max- flow Socialwelfare s.t.

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Decomposition Relax the variables to [0,1], getting a linear program (LPR) If the integrality gap between the integer program (IP) and the LPR is at most, we can decompose the optimal solution as feasible assignment

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Decomposition (cont’d), we can view this decomposition as a probability distribution over the integer solutions, where a feasible channel assignment is selected with probability, we can view this decomposition as a probability distribution over the integer solutions, where a feasible channel assignment is selected with probability

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Randomized channel assignment: done! Payment?

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Payment A VCG-like payment is used for ensuring truthfulness (in expectation) and approximately maximizing social welfare:

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Results Theorem: The randomized auction is truthful in expectation. Theorem: The randomized auction achieves optimal social welfare in expectation.

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Simulation results

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Auction efficiency with different numbers of SNs enrolled

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Auction efficiency with different sizes of SNs

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Auction efficiency with different auction settings

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Conclusions Generalized secondary users Provable truthfulness Performance-guaranteed social welfare Improved spectrum utilization

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Thank You google “iQua Toronto”

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