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:
Interference
considered
Sort SNs:
Greedily assign channels to shortest
paths as long as there are channels
feasible for assignment
•
Our idea: Payment
Get a winner i’s “critical bid”:
Set bi 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:
A toy example
Payment:
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:
1.monotonic winner determination
2.bid-independent pricing
•
(Myerson’s characterization (1981))
A randomized auction
Problem formulation
An integer program:
Social
welfare
s.t.
•
Winner determination to weighted maxflow
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
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
Thank You
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