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

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

Need for multi-hop support ╳

Multi-hop transmission

What are the difficulties for multi-hop supported auctions?

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

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

A heuristic truthful auction

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

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:

Payment: A toy example

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))

A randomized auction

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

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

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

Randomized channel assignment: done! Payment?

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

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

Simulation results

Auction efficiency with different numbers of SNs enrolled

Auction efficiency with different sizes of SNs

Auction efficiency with different auction settings

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

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