Spectrum Sharing Games of
Network Operators and Cognitive Radios
Jean-Pierre Hubaux
EPFL
Work done in collaboration with
M. H. Manshaei, M. Felegyhazi, J. Freudiger, and P. Marbach
1
Contents
1.
2.
3.
Spectrum allocation and usage
Introduction to game theory
Spectrum sharing games
–
–
–
4.
Network operators
•
Asymmetric network operators
•
Border games of cellular operators
•
Operators in shared spectrum
Unlicensed bands
•
Asymmetric wireless systems
•
WiFi operators
Cognitive radios
•
Opportunistic spectrum sharing
•
Auction based spectrum sharing
•
Multi-Cell OFDM spectrum sharing
Conclusion
2
1. Spectrum allocation and usage
Measured Spectrum Occupancy Averaged over Six Locations
PLM, Amateur, others: 30-54 MHz
TV 2-6, RC: 54-88 MHz
Air traffic Control, Aero Nav: 108-138 MHz
Fixed Mobile, Amateur, others:138-174 MHz
TV 7-13: 174-216 MHz
Maritime Mobile, Amateur, others: 216-225 MHz
Fixed Mobile, Aero, others: 225-406 MHz
Amateur, Fixed, Mobile, Radiolocation, 406-470 MHz
TV 14-20: 470-512 MHz
TV 21-36: 512-608 MHz
TV 37-51: 608-698 MHz
TV 52-69: 698-806 MHz
Cell phone and SMR: 806-902 MHz
Unlicensed: 902-928 MHz
Paging, SMS, Fixed, BX Aux, and FMS: 928-906 MHz
IFF, TACAN, GPS, others: 960-1240 MHz
Amateur: 1240-1300 MHz
Aero Radar, Military: 1300-1400 MHz
Space/Satellite, Fixed Mobile, Telemetry: 1400-1525 MHz
Mobile Satellite, GPS, Meteorologicial: 1525-1710 MHz
Fixed, Fixed Mobile: 1710-1850 MHz
PCS, Asyn, Iso: 1850-1990 MHz
TV Aux: 1990-2110 MHz
Common Carriers, Private, MDS: 2110-2200 MHz
Space Operation, Fixed: 2200-2300 MHz
Amateur, WCS, DARS: 2300-2360 MHz
Telemetry: 2360-2390 MHz
U-PCS, ISM (Unlicensed): 2390-2500 MHz
ITFS, MMDS: 2500-2686 MHz
Surveillance Radar: 2686-2900 MHz
0.0%
25.0%
50.0%
75.0%
100.0%
Spectrum Occupancy
©Shared spectrum company report, August 2005
Locations: New York city; Riverbend Park, Great Falls, VA; Tysons Corner, VA
NSF Roof, Arlington, VA; NRAO, Greenbank, WV; SSC Roof, Vienna, VA
In Europe, cellular operators have spent nearly 100 billion Euros to buy
3
rd
spectrum for the 3 generation
Real-time airwaves auction model
• Proposal by Google, inspired by their online
advertising auction
• Filed to FCC in May 2007
• Would allow commercial operators (including small
ones) to bid for access to spectrum controlled by the
actual licensee
• Supposed to improve spectrum use and create a
robust market for innovative digital services
4
2. Brief introduction to Game Theory
• Discipline aiming at modeling situations in which
actors have to make decisions which have mutual,
possibly conflicting, consequences
• Classical applications: economics, but also politics
and biology
• Example: should a company invest in a new plant, or
enter a new market, considering that the
competition may make similar moves?
• Most widespread kind of game: non-cooperative
(meaning that the players do not attempt to find an
agreement about their possible moves)
5
Classification of games
Non-cooperative
Cooperative
Static
Dynamic (repeated)
Strategic-form
Extensive-form
Perfect information
Imperfect information
Complete information
Incomplete information
Perfect info: each player knows the identity of other players and, for each
of them, the payoff resulting of each strategy.
Complete info: each player can observe the action of each other player.
6
Static (or “single-stage”) games
7
Example 1: The Forwarder’s Dilemma
?
Blue
Green
?
8
E1: From a problem to a game
• users controlling the devices are rational = try to
maximize their benefit
• game formulation: G = (P,S,U)
– P: set of players
– S: set of strategy functions
– U: set of utility functions
• Reward for packet reaching
the destination: 1
• Cost of packet forwarding:
c (0 < c << 1)
• strategic-form representation
Green
Forward
Blue
Drop
Forward
(1-c, 1-c)
(-c, 1)
Drop
(1, -c)
(0, 0)
9
Solving the Forwarder’s Dilemma (1/2)
Strict dominance: strictly best strategy, for any strategy of the other player(s)
Strategy si strictly dominates if
ui ( si' , si )  ui ( si , si ), si  S i , si'  Si
where:
ui U
utility function of player i
si  Si strategies of all players except
player i
In Example 1, strategy Drop strictly dominates strategy Forward
Green
Forward
Blue
Drop
Forward
(1-c, 1-c)
(-c, 1)
Drop
(1, -c)
(0, 0)
10
Solving the Forwarder’s Dilemma (2/2)
Solution by iterative strict dominance:
Green
Forward
Blue
Forward
Drop
(1-c, 1-c)
(1, -c)
Drop
(-c, 1)
(0, 0)
Drop strictly dominates Forward
BUT
}
Dilemma
Forward would result in a better outcome
Result: Tragedy of the commons ! (Hardin, 1968)
11
Example 2: The Joint Packet Forwarding Game
Source
?
?
Green
Blue
• Reward for packet reaching
the destination: 1
• Cost of packet forwarding:
c (0 < c << 1)
Green
Forward
Blue
Forward
Drop
(1-c, 1-c)
(0, 0)
Dest
Drop
(-c, 0)
(0, 0)
No strictly dominated strategies !
12
E2: Weak dominance
Weak dominance: strictly better strategy for at least one opponent strategy
Strategy s’i is weakly dominated by strategy si if
ui ( si' , si )  ui ( si , si ), si  S i
with strict inequality for at least one s-i
Source
?
?
Green
Blue
Dest
Green
Iterative weak dominance
BUT
Blue
Forward
Drop
Forward
(1-c, 1-c)
(0, 0)
(-c, 0)
(0, 0)
Drop
The result of the iterative weak
dominance is not unique in general !
13
Nash equilibrium (1/2)
Nash Equilibrium: no player can increase its utility by deviating unilaterally
Green
Forward
Blue
E1: The Forwarder’s
Forward
Dilemma
Drop
(1-c, 1-c)
(1, -c)
Green
Forward
Blue
E2: The Joint Packet
Forward
Forwarding game
Drop
(1-c, 1-c)
(0, 0)
Drop
(-c, 1)
(0, 0)
Drop
(-c, 0)
(0, 0)
14
Nash equilibrium (2/2)
Strategy profile s* constitutes a Nash equilibrium if, for each player i,
ui ( s , s )  ui ( si , s ), si  Si
*
i
where:
*
i
ui U
si  Si
*
i
utility function of player i
strategy of player i
The best response of player i to the profile of strategies s-i is
a strategy si such that:
bi ( si )  arg max ui ( si , si )
si Si
Nash Equilibrium = Mutual best responses
Caution! Many games have more than one Nash equilibrium
15
Example 3: The Multiple Access game
Time-division channel
Reward for successful
transmission: 1
Green
Blue
Quiet
Cost of transmission: c
(0 < c << 1)
Transmit
Quiet
Transmit
(0, 0)
(1-c, 0)
(0, 1-c)
(-c, -c)
There is no strictly dominating strategy
There are two Nash equilibria
16
E3: Mixed strategy Nash equilibrium
p: probability of transmit for Blue
q: probability of transmit for Green
ublue  p(1  q)(1  c)  pqc  p(1  c  q)
u green  q (1  c  p )
objectives
–
Blue: choose p to maximize ublue
– Green: choose q to maximize ugreen
p  1  c, q  1  c
is a Nash equilibrium
17
Example 4: The Jamming game
transmitter
two channels:
C1 and C2
jammer
Green
Blue
C1
C2
C1
C2
(-1, 1)
(1, -1)
(1, -1)
(-1, 1)
There is no pure-strategy
Nash equilibrium
1
1
p  , q  is a Nash equilibrium
2
2
transmitter:
• reward for successful
transmission: 1
• loss for jammed
transmission: -1
jammer:
• reward for successful
jamming: 1
• loss for missed
jamming: -1
p: probability of transmit
on C1 for Blue
q: probability of transmit
on C1 for Green
18
Theorem by Nash, 1950
Theorem: Every finite strategic-form game has a
mixed-strategy Nash equilibrium.
19
Efficiency of Nash equilibria
Green
Forward
Blue
E2: The Joint
Packet Forwarding
game
Forward
Drop
(1-c, 1-c)
(0, 0)
Drop
(-c, 0)
(0, 0)
How to choose between several Nash equilibria ?
Pareto-optimality: A strategy profile is Pareto-optimal if it is not
possible to increase the payoff of any player without decreasing the
payoff of another player.
20
How to study Nash equilibria ?
Properties of Nash equilibria to investigate:
•
•
•
•
existence
uniqueness
efficiency (Pareto-optimality)
emergence (dynamic games, agreements)
21
Repeated games
22
Repeated games
• repeated interaction between the players (in stages)
• move: decision in one interaction
• strategy: defines how to choose the next move, given
the previous moves
• history: the ordered set of moves in previous stages
– most prominent games are history-1 games (players
consider only the previous stage)
• initial move: the first move with no history
• finite-horizon vs. infinite-horizon games
• stages denoted by t (or k)
23
Strategies in the repeated game
• usually, history-1 strategies, based on different inputs:
– others’ behavior:
mi  t  1  si  mi  t  
– others’ and own behavior:
– utility:
mi  t  1  si  mi  t  , mi  t  
mi  t  1  si ui  t  
Example strategies in the Forwarder’s Dilemma:
Blue (t)
initial
move
F
D
strategy name
Green (t+1)
F
F
F
AllC
F
F
D
Tit-For-Tat (TFT)
D
D
D
AllD
F
D
F
Anti-TFT
24
The Repeated Forwarder’s Dilemma
?
Green
Blue
?
Green
Forward
Blue
Drop
Forward
(1-c, 1-c)
(-c, 1)
Drop
(1, -c)
(0, 0)
stage payoff
25
Analysis of the
Repeated Forwarder’s Dilemma

infinite game with discounting:
ui   ui  t    t
t 0
Blue strategy
Green strategy
Blue utility
Green utility
AllD
AllD
0
0
AllD
TFT
1
-c
AllD
AllC
1/(1-ω)
-c/(1-ω)
AllC
AllC
(1-c)/(1-ω)
(1-c)/(1-ω)
AllC
TFT
(1-c)/(1-ω)
(1-c)/(1-ω)
TFT
TFT
(1-c)/(1-ω)
(1-c)/(1-ω)
26
Conclusion on game theory
• Game theory can help modeling greedy behavior in
wireless networks
• Discipline still in its infancy
• Alternative solutions
– Ignore the problem
– Build protocols in tamper-resistant hardware
27
http://secowinet.epfl.ch
For the tutorial on game theory:
28
M. Felegyhazi and J.-P. Hubaux, Game Theory in Wireless Networks: A Tutorial
Technical report – 2006 [LCA-REPORT-2006-002]
Book structure
Security
Cooperation
12. Behavior enforcement
8. Privacy protection
11. Operators in shared spectrum
7. Secure routing
10. Selfishness in PKT FWing
6. Secure neighbor discovery
9. Selfishness at MAC layer
5. Security associations
4. Naming and addressing
3. Trust
Appendix A:
Security and crypto
2. Upcoming networks
1. Existing networks
Appendix B:
Game theory
29
Who is malicious? Who is selfish?
Harm everyone: viruses,…
Selective harm: DoS,…
Big brother
Spammer
Cyber-gangster:
phishing attacks,
trojan horses,…
Greedy operator
Selfish mobile station
There is no watertight boundary between malice and selfishness
 Both security and game theory approaches can be useful
30
From discrete to continuous
Warfare-inspired Manichaeism:
0
1
Bad guys (they)
Attacker
Good guys (we)
System (or country) to be defended
The more subtle case of commercial applications:
0
1
Undesirable
behavior
Desirable
behavior
• Security often needs incentives
• Incentives usually must be secured
31
Another book:
Cognitive Wireless Networks: Concepts, Methodologies and Visions
- Inspiring the Age of Enlightenment of Wireless Communications –
Edited by Frank H. P. Fitzek and Marcos D. Katz
Part I:
Introductory Chapter
Part II:
Cooperative Networks: Social, Operational
and Communicational Aspects
Part III: Cognitive Networks
Part IV: Marrying Cooperation and Cognition
in Wireless Networks
Part V: Methodologies and Tools
Part VI: Visions, Prospects and
Emerging Technologies
32
List of Contributors
Aachen University, Germany
AIST, Japan
Budapest University of Technology and Economics, Hungary
Create-NET, Italy
DoCoMo Euro-Labs, Germany
EPFL, Switzerland
Harvard University, USA
Konica Italia, Italy
KTH, Sweden
MIT, USA
Motorola Labs, France
Oxford University, UK
Stevens Institute of Technology, USA
Technical University of Catalonia, Spain
Technical University of Denmark, Denmark
Universität Duisburg Essen, Germany
Universität Karlsruhe, Germany
University of Aalborg, Denmark
University of Bologna, Italy
University of California at Berkeley, USA
University of California, San Diego, USA
University of Dresden, Germany
University of Paderborn, Germany
University of Padova, Italy
University of Piraeus, Greece
VTT, Finland
WINLAB and Rutgers University, USA
33
3. Spectrum sharing games
Spectrum Sharing Games in
Unlicensed Band
Licensed Band
Cellular Operators
Unlicensed Band
Devices
Cognitive
Radios
• WAN-WiFi competition/cooperation
• Heterogeneous wireless systems
(University of Texas at Austin)
(University of California at Berkeley)
• Cellular operators near national borders (EPFL)
• Wifi Operators (Bell LAB, MIT)
• Cellular operators in shared spectrum (EPFL)
• Opportunistic spectrum sharing (UCSB)
• Auction based spectrum sharing (Northwestern)
• Multi-Cell OFDM spectrum sharing (University of Maryland)
34
3.1 Spectrum Sharing Games of
Network Operators
1.
2.
3.
A. Zemlianov and G. de Veciana, “Cooperation and Decision Making in
Wireless Multi-provider Setting,” INFOCOM 2005
M. Felegyhazi et al., “Border Games in Cellular Networks,” INFOCOM
2007
M. Felegyhazi and J.-P. Hubaux, “Wireless Operators in a Shared
Spectrum,” INFOCOM 2006
35
3.1.1 WAN-WiFi competition/cooperation
(University of Texas at Austin)
36
Switch decision
Switch from WLAN to WAN
Switch from WAN to WLAN
Nkh: number of users connected to hotspot hk
Smw: number of users connected to base station wm
ch: cost of switching to a hotspot AP
cw: cost of switching to a WAN AP
t: decision time
37
Results
•
•
•
•
Given any initial configuration of agents’ choices, the
system converges to an equilibrium configuration as
t∞
This equilibrium is not necessarily unique
The class of payoff functions that are congestion
dependent provide much better performance to users on
average than the simple proximity-based decision
strategy
The results can notably help operators with both
wireless WAN infrastructure (e.g., WiMAX) and a set of
WiFi hotspots to optimize their network
38
3.1.2 Border games of cellular networks (EPFL)
Example:
Mobile users in Geneva airport have
access to two service providers
in the same frequency.
Other examples:
- Slovenia and Croatia
- Finland and Russia
- USA and Mexico (San Diego)
- USA and Canada (Detroit)
- Jordan and Israel
- Hong-Kong and China
39
Border games of cellular operators
•
•
•
Two CDMA operators: A and B
Adjust the pilot signals
Power control game (no power
cost):
–
–
–
players = operators
strategies = pilot powers
payoffs = attracted users (best
SINR)
Gppilot
Signal-to-interference-plus-noise ratio:
SINRAvpilot 

G ppilot  PA  d Av
pilot
pilot
N 0 W  I own
 I other
Own-cell interference
pilot
I own



   d Av
T
  Aw 
 wM A

Other-to-own-cell interference


pilot

I other
   d Bv
P

T
 B  Bw 
wM B


where: Gppilot – pilot processing gain
PA

d Av


TAw
MA
– pilot signal power of BS A
– path loss between A and v
– own-cell interference factor
– other-to-own-cell interference factor
– traffic signal power assigned to w
by BS A
40
– set of users attached to BS A
Results (1): Incentives for operators to be strategic
41
Results (2): Existence of a unique maximum payoff
when both operators are strategic
42
Results (3): Best response calculation for two players
• Unique and Pareto-optimal Nash equilibrium
• Higher pilot power than in the standard Ps = 2W
• 10 users in total
standard
Nash equilibrium
43
Other results
1. Price of anarchy and price of conformance to evaluate NE
2. Extend payoff function to consider the cost of high pilot power
 leads to a Prisoner’s dilemma situation
U – fair payoff (half of the users)
D – payoff difference by selfish behavior
C* - cost for higher pilot power
44
3.1.3 Operators in a shared spectrum (EPFL)
•
•
•
•
•
•
•
•
•
two operators: A and B
set of base stations: BA and BB
base stations are placed on the vertices of a
grid
each base station of A has the same radio
range rA (relaxed later), same for B
base stations emit pilot signals on the same
channel, with the radio ranges: rA, rB
full coverage by combination of the two
operator’s coverage
maximum power limit PMAX → RMAX
if
2
rA  rB  RMIN 
d
2
devices have omnidirectional antennas
45
System model
•
•
•
A set of users uniformly distributed in the area
Free roaming
Users attach to the base station with the best
pilot signal


Pi  g iu


max 
Pi
N 0   Pj  g ju 


j


where the channel gain: g iu 
•
1
d iu2
Operators want to cover the largest area with
their pilot signal
46
Power control game
•
•
•
•
static game G = (P, S, U)
Players → operators
Strategy → pilot signal radio range
Utility: coverage area of their own pilot
signal minus the interference area
U i  Oi   i  Yi
where γi is the cooperation
parameter of player i:
• cooperativeness
• agreement
• power price
47
Repeated game and punisher strategy
•
Punisher strategy: Play RMIN in the first time step. Then
for each time step:
–
play RMIN, if the other player played RMIN
– play RMAX for the next ki time steps, if the other player
played anything else
48
What is the right cooperation model ?
• Non-cooperative games: no trust and no agreement
between players
• Cooperative games: players talk to each other and try
to find an agreement
• Cooperation is often assumed at the physical layer
(e.g. for beamforming)
• Non-cooperative behavior is often (but not always)
assumed at the MAC, network, and transport layers
49
A glimpse at IEEE JSAC
• Cooperative Communications and
Networking – Vol. 25 (2007), issue 2
• Adaptive, Spectrum Agile and Cognitive
Wireless Networks – Vol. 25 (2007), issue 3
• Non-Cooperative Behavior in Networking –
to appear in Q3 2007
• Game Theory in Communication Systems –
submission due date: August 1, 2007
50
Panel at Mobicom 2007
(Montreal, September 13)
Chimpanzee
www.ncbi.nlm.nih.gov
Bonobo
www.bio.davidson.edu
Bonobos Vs Chimps: Cooperative and Non-Cooperative
Behavior in Wireless Networks
Panelists:
Jean-Pierre Hubaux, EPFL (organizer and moderator)
Ramesh Johari, Stanford University
P. R. Kumar, UIUC
Joseph Mitola, MITRE Corp.
Heather Zheng, UCSB
51
Conclusion
• Potential of the area fuelled by:
– The emergence of cognitive radios
– The willingness to revisit the way spectrum is allocated
– The rise of WiFi community networks
• Limitations of game theory modeling for wireless
networks
– Information for the players: games are in reality of
incomplete and imperfect information
– Expression of payoffs (benefits and costs)
– Cooperative Vs non-cooperative games
– Reputation of players
http://winet-coop.epfl.ch
52