Singleton Spectrum Mobility Games with
Incomplete Information
Presenter: Qingkai Liang
Department of Electronic Engineering
Shanghai Jiao Tong University, China
Outline
Introduction
System Model
Complete-Information Scenario
Incomplete-Information Scenario
Simulation Results
Conclusion and Future Work
Singleton Spectrum Mobility Games with Incomplete Information
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Introduction
 What is the problem solved in the paper?
 Spectrum Mobility in the Cognitive Radio Network
Primary User 1
Secondary User 1
Lease
Secondary User 2
Licensed to
Channel 1
Licensed to
Lease
Secondary User 3
Channel 2
Channel 3
Lease
Channel 4
Licensed to
Primary User 2
Primary User 3
Licensed to
Secondary User 4
Primary User 4
Lease
Secondary Users can only transmit on those licensed
channels when Primary Users do not occupy them!
Singleton Spectrum Mobility Games with Incomplete Information
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Introduction
 What is the problem solved in the paper?
 Spectrum Mobility in the Cognitive Radio Network
Primary User 1
Secondary User 1
Lease
Secondary User 2
Licensed to
Channel 1
Licensed to
Lease
Secondary User 3
Channel 2
Channel 3
Lease
Channel 4
Licensed to
Primary User 2
Primary User 3
Licensed to
Secondary User 4
Primary User 4
Lease
What happens when Primary Users reclaim their
licensed channels?
Singleton Spectrum Mobility Games with Incomplete Information
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Introduction
 What is the problem solved in the paper?
 Spectrum Mobility in the Cognitive Radio Network
Primary User 1
Secondary User 1
Lease
Secondary User 2
Reclaim
Channel 1
Reclaim
Lease
Secondary User 3
Channel 2
Channel 3
Lease
Channel 4
Licensed to
Primary User 2
Primary User 3
Licensed to
Secondary User 4
Primary User 4
Lease
Spectrum Handoff (Channel Switching) takes place!
How to avoid potential congestion in the channel selection?
Singleton Spectrum Mobility Games with Incomplete Information
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Introduction
 What is the problem solved in the paper?
 How to re-select one switch-to channel when the spectrum
environment varies?
 Channel condition
 Interference from users who choose the same channel
 Incentive-aware
 Distributed
The problem is formulated as a Singleton Spectrum Mobility Game
A Congestion Game
Singleton Spectrum Mobility Games with Incomplete Information
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Introduction
 Congestion Games
 Aim at minimizing the potential costs for using the facilities
 Singleton Congestion Games
 Each player only selects one facility
Singleton Spectrum Mobility Games with Incomplete Information
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Related Works
Some previous works have focused on the channel re-selection problem
in the spectrum mobility management, using the game theory.
[1] R. Southwell, J. Huang and X. Liu, “Spectrum Mobility Games”, IEEE
INFOCOM, 2012.
[2] I. Malanchini, M. Cesana, and N. Gatti, “On Spectrum Selection
Games in Cognitive Radio Networks,” IEEE GLOBECOM, 2009.
[3] Y. B. Reddy, H. Smith, and M. Terrell, “Congestion Game Models for
Capacity and Bandwidth Relation in Dynamic Spectrum Access,” ITNG,
2010.
Singleton Spectrum Mobility Games with Incomplete Information
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Related Works
 Common Drawbacks




Homogeneous secondary users (players)
Homogeneous channels (facilities)
Assume secondary users’ complete information
No refinement of the Nash Equilibriums
Singleton Spectrum Mobility Games with Incomplete Information
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Contributions
 Interesting Points
 Heterogeneous secondary users (players)
 Heterogeneous channels (facilities)
 Two information scenarios
 Complete Information
 Incomplete Information
Maximize average
SINR of all users
Rarely discussed
due to its difficulty!
Neglected by
previous works
 Find the socially optimal Nash Equilibrium in polynomial time!
 Finding the socially optimal equilibrium in the congestion games was proved to
be NP-hard in general cases! [4]
[4] D. Fotakis, C. K. Spyros , E. Koutsoupias, M. Mavronicolas, and G. S. Paul, “The
structure and complexity of Nash equilibria for a selfish routing game,” ICALP, 2002.
Singleton Spectrum Mobility Games with Incomplete Information
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Outline
Introduction
System Model
Complete-Information Scenario
Incomplete-Information Scenario
Simulation Results
Conclusion and Future Work
Singleton Spectrum Mobility Games with Incomplete Information
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System Model
 Physical Model







M heterogeneous and orthogonal channels (denoted by Ci )
Channel Ci has AWGN of power  i
N heterogeneous secondary users (denoted by SU k )
Each SU is equipped with a pair of transmitter and receiver
SU k can cause interference of level I k to users in the same channel
Signal strength perceived at each SU’s receiver: Pk
SINR perceived by SU k is it selects channel Ci :
k
A ( k ) i

i 
Pk

nM \{k }: A( n ) i
In
Singleton Spectrum Mobility Games with Incomplete Information
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System Model
 Bayesian Spectrum Mobility Game Model
 Game Formulation
G  {M , N , T , A, p,}
Player’s type spaces
Player’s strategy space
Player’s type distribution
(belief)
Player’s interference
information
Singleton Spectrum Mobility Games with Incomplete Information
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Outline
Introduction
System Model
Complete-Information Scenario
Incomplete-Information Scenario
Simulation Results
Conclusion and Future Work
Singleton Spectrum Mobility Games with Incomplete Information
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Complete-Information Scenario
 Each SU has full knowledge about others’ interference
information

Theorem 1: There’s at least one Nash Equilibrium in the
singleton spectrum mobility games with complete
information.
Singleton Spectrum Mobility Games with Incomplete Information
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Complete-Information Scenario
 May exist multiple Nash Equilibriums
 Evaluation of Nash Equilibriums

 Socially optimal Nash Equilibrium: yield the maximum social
welfare among all equilibriums
 The following algorithm computes the socially optimal Nash
Equilibrium in polynomial time
Singleton Spectrum Mobility Games with Incomplete Information
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Complete-Information Scenario
Time complexity
O( M 3 N 2 )
Space complexity
O( M 2 N )
Singleton Spectrum Mobility Games with Incomplete Information
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Complete-Information Scenario
Theorem 2: Algorithm 2 can compute the social optimal
Nash Equilibrium of the singleton spectrum mobility game
in the complete-information scenario.
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Outline
Introduction
System Model
Complete-Information Scenario
Incomplete-Information Scenario
Simulation Results
Conclusion and Future Work
Singleton Spectrum Mobility Games with Incomplete Information
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Incomplete-Information Scenario
 Based on the results in the complete-information case

 The following algorithm computes the socially optimal
Bayesian Nash Equilibrium in the incomplete-information
scenario in polynomial time
Singleton Spectrum Mobility Games with Incomplete Information
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Incomplete-Information Scenario
Theorem 3: Algorithm 3 can compute the social optimal
Bayesian Nash Equilibrium for the singleton spectrum
mobility games with incomplete information.
Singleton Spectrum Mobility Games with Incomplete Information
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Outline
Introduction
System Model
Complete-Information Scenario
Incomplete-Information Scenario
Simulation Results
Conclusion and Future Work
Singleton Spectrum Mobility Games with Incomplete Information
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Simulation Results
Singleton Spectrum Mobility Games with Incomplete Information
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Simulation Results
Singleton Spectrum Mobility Games with Incomplete Information
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Simulation Results
Singleton Spectrum Mobility Games with Incomplete Information
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Simulation Results
Singleton Spectrum Mobility Games with Incomplete Information
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Outline
Introduction
System Model
Complete-Information Scenario
Incomplete-Information Scenario
Simulation Results
Conclusion and Future Work
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Future Work




The stability of the Nash Equilibrium
The analysis of the price of anarchy
Repeated game
Multi-channel selection
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Thank you !