TRUST:A General Framework
for Truthful Double
Spectrum Auctions
Xia Zhou and Heather Zheng
Department of Computer Science, University of California,
Santa Barbara, CA 93106
IEEE INFOCOM (2009)
Introduction

Well-designed auctions provide fairness
and efficiency
◦ In the past decade, the FCC have been using
single-sided auctions to allocate spectrum

In order to improve spectrum utilization,
a new spectrum double auction
framework is proposed
◦ Exploit spatial reusability
2
Introduction

Reusability makes spectrum different
from conventional goods and difficult to
design
◦ Conventional auctions do not consider
reusability[1][14]
◦ Spectrum auctions only consider singlesided[25]
[1] BABAIOFF, M., AND NISAN, N. Concurrent auctions across the supply chain. In Proc. of Economic Commerce (2001).
[14] MCAFEE, R. P. A dominant strategy double auction. Journal of Economic Theory 56, 2 (April 1992), 434–450.
[25] ZHOU, X., GANDHI, S., SURI, S., AND ZHENG, H. eBay in the sky: Strategy-proof wireless spectrum auctions. In Proc.
of MobiCom (Sept. 2008).
3
Introduction

A framework for truthful double
spectrum auction(TRUST) is proposed
◦ Integrate spectrum allocation and pricing
components to improve spectrum utilization
◦ TRUST can use any spectrum allocation
algorithm
◦ TRUST guarantees three economic properties,
truthfulness, individual rationality and ex-post
budget balance
4
Double Spectrum Auction Problems
－Problem Model

The goal is to improve spectrum
utilization and to achieve economic
properties
◦ Consider single-round double spectrum
auction
◦ One auctioneer, M sellers, N buyers
◦ Same time term
◦ Sealed-bid and private
5
Double Spectrum Auction Problems
－Required Economic Properties
three critical properties required to
design economic-robust double auctions
 Truthfulness

◦ No seller m or buyer n can improve its own
utility by bidding untruthfully

Individual Rationality
◦ No winning seller is paid less than its bid and
no winning buyer pays more than its bid

Ex-Post Budget Balance
◦ The auctioneer’s profit ≧0
6
Challenges of Double Spectrum
Auction Design

Some truthful auction designs
[1]
[14]
[25]
[1] BABAIOFF, M., AND NISAN, N. Concurrent auctions across the supply chain. In Proc. of Economic Commerce (2001).
[14] MCAFEE, R. P. A dominant strategy double auction. Journal of Economic Theory 56, 2 (April 1992), 434–450.
[25] ZHOU, X., GANDHI, S., SURI, S., AND ZHENG, H. eBay in the sky: Strategy-proof wireless spectrum auctions. In Proc.
of MobiCom (Sept. 2008).
7
Challenges of Double Spectrum
Auction Design

McAfee double auction
◦ Sort bids in non-decreasing (for sellers) and
non-increasing (for buyers) orders
◦
◦ The first (k − 1) sellers and the first (k − 1)
buyers are the auction winners
◦ All winning buyers are charged
◦ All winning sellers are paid
8
TRUST－Design Rationale

It follows McAfee’s design and combines
reusability
◦ Map a group of buyers into each seller
In TRUST, form buyer groups based on
their interference condition
 Uniform pricing within each buyer group
 Group bid≦lowest bid*number of buyers

9
TRUST－Design Details
TRUST performs the auction in three
steps
 Step 1:Buyer group formation

◦ Buyers assigned to the same channel are
organized into the same group
◦ Use different spectrum allocation algorithms
to cope with various interference models
10
TRUST－Design Details

Step 2:Winner Determination
◦ Each group is a “super buyer” and has a
“group bid( )”
 Gl : represent one of the groups
 nl : number of buyers in the group l
◦ As McAfee, sort the seller bids and group bids
and determine k
11
TRUST－Design Details

Step 3:Pricing
◦ As McAfee, each winning seller is paid kth
seller’s bid, and each winning group should
pay kth group’s bid
◦ The group price is shared among all buyers in
the group:
◦ The auctioneer’s profit is:
12
TRUST－an Illustrative Example
OPT : optimal algorithm to minimize the number of channels
 RAND : randomly produced allocation result

13
TRUST－Proof of Auction Properties

Ex-post budget balanced
◦ Because k is the largest index satisfies that
buyer’s bid ≧seller’s bid

Individual rational
◦ Because the sort, buyers pay less than their
bids and sellers get more than their bids
14
TRUST－Proof of Auction Properties

Truthfulness
◦ Lemma 1. if buyer n wins by bidding Bn , then also
wins by bidding Bn’> Bn
◦ Lemma 2. if seller m wins by bidding Bm, then also
wins by bidding Bm’< Bm
◦ Lemma 3. if buyer n wins by bidding Bn and Bn’, the
price Pn charged to n is the same for both
◦ Lemma 4. if seller m wins by bidding Bm and Bm’,
then the payment Pm to m is the same for both
15
TRUST－Proof of Auction Properties

Truthfulness (for buyer)
◦ Any buyer n cannot obtain higher utility by
bidding Bn’≠Vn
 Case1. both get zero utility
 Case2. happens if Bn’<Vn. Bn’ bidder gets no utility
 Case3. happens if Bn’>Vn. When Bn’ bidder wins,
he should pay Vn<p<Bn’ ∴utility<0
 Case4. both get the same utility
16
Experimental Results－
Simulation Setup

Allocation algorithm
◦
◦
◦
◦

Max-IS[21]
Greedy-U[17]
Greedy[17]
RAND
Interference condition
◦ Random
◦ Clustered
[17] RAMANATHAN, S. A unified framework and algorithm for channel assignment in wireless
networks. Wirel. Netw. 5, 2 (1999), 81–94.
[21] SUBRAMANIAN, A. P., GUPTA, H., DAS, S. R., AND BUDDHIKOT,
M. M. Fast spectrum allocation in coordinated dynamic spectrum access
based cellular networks. In Proc. of IEEE DySPAN (November 2007).
17
Experimental Results－
Economic Impact on Spectrum Distribution

Compare TRUST to PA(Pure Allocation)

Causes: choice of winning groups
18
Experimental Results－
Choosing Allocation Algorithm in TRUST
An effective allocation is important to
TRUST
 Limit the size of each group

19
Conclusion
TRUST achieves truthfulness, individual
nationality and ex-post budget balance,
and enable spectrum reuse
 Tradeoff between spectrum efficiency
and economic robustness

20