1

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

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1. Spectrum allocation and usage2. Introduction to game theory3. Spectrum sharing games

– 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

4. Conclusion

Contents

3

Measured Spectrum Occupancy Averaged over Six Locations

0.0% 25.0% 50.0% 75.0% 100.0%

PLM, Amateur, others: 30-54 MHzTV 2-6, RC: 54-88 MHz

Air traffic Control, Aero Nav: 108-138 MHzFixed Mobile, Amateur, others:138-174 MHz

TV 7-13: 174-216 MHzMaritime Mobile, Amateur, others: 216-225 MHz

Fixed Mobile, Aero, others: 225-406 MHzAmateur, Fixed, Mobile, Radiolocation, 406-470 MHz

TV 14-20: 470-512 MHzTV 21-36: 512-608 MHzTV 37-51: 608-698 MHzTV 52-69: 698-806 MHz

Cell phone and SMR: 806-902 MHzUnlicensed: 902-928 MHz

Paging, SMS, Fixed, BX Aux, and FMS: 928-906 MHzIFF, TACAN, GPS, others: 960-1240 MHz

Amateur: 1240-1300 MHzAero Radar, Military: 1300-1400 MHz

Space/Satellite, Fixed Mobile, Telemetry: 1400-1525 MHzMobile Satellite, GPS, Meteorologicial: 1525-1710 MHz

Fixed, Fixed Mobile: 1710-1850 MHzPCS, Asyn, Iso: 1850-1990 MHz

TV Aux: 1990-2110 MHzCommon Carriers, Private, MDS: 2110-2200 MHz

Space Operation, Fixed: 2200-2300 MHzAmateur, WCS, DARS: 2300-2360 MHz

Telemetry: 2360-2390 MHzU-PCS, ISM (Unlicensed): 2390-2500 MHz

ITFS, MMDS: 2500-2686 MHzSurveillance Radar: 2686-2900 MHz

Spectrum Occupancy

©Shared spectrum company report, August 2005

In Europe, cellular operators have spent nearly 100 billion Euros to buy spectrum for the 3rd generation

1. Spectrum allocation and usage

Locations: New York city; Riverbend Park, Great Falls, VA; Tysons Corner, VANSF Roof, Arlington, VA; NRAO, Greenbank, WV; SSC Roof, Vienna, VA

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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

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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)

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Classification of games

Non-cooperative Cooperative

Static Dynamic (repeated)

Strategic-form Extensive-form

Perfect information Imperfect information

Complete information Incomplete information

Cooperative

Imperfect information

Incomplete information

Perfect info: each player knows the identity of other players and, for eachof them, the payoff resulting of each strategy.

Complete info: each player can observe the action of each other player.

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Static (or “single-stage”) games

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Example 1: The Forwarder’s Dilemma

?

?

Blue Green

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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

• strategic-form representation

• Reward for packet reaching the destination: 1• Cost of packet forwarding: c (0 < c << 1)

(1-c, 1-c) (-c, 1)

(1, -c) (0, 0)

BlueGreen

Forward

Drop

Forward Drop

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Solving the Forwarder’s Dilemma (1/2)

' '( , ) ( , ), ,i i i i i i i i i iu s s u s s s S s S

iu Ui is S

Strict dominance: strictly best strategy, for any strategy of the other player(s)

where: utility function of player i

strategies of all players except player i

In Example 1, strategy Drop strictly dominates strategy Forward

(1-c, 1-c) (-c, 1)

(1, -c) (0, 0)

BlueGreen

Forward

Drop

Forward Drop

Strategy strictly dominates ifis

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Solving the Forwarder’s Dilemma (2/2)

Solution by iterative strict dominance:

(1-c, 1-c) (-c, 1)

(1, -c) (0, 0)

BlueGreen

Forward

Drop

Forward Drop

Result: Tragedy of the commons ! (Hardin, 1968)

Drop strictly dominates ForwardDilemma

Forward would result in a better outcomeBUT }

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Example 2: The Joint Packet Forwarding Game

?Blue GreenSource Dest

?

No strictly dominated strategies !

• Reward for packet reaching the destination: 1• Cost of packet forwarding: c (0 < c << 1)

(1-c, 1-c) (-c, 0)

(0, 0) (0, 0)

BlueGreen

Forward

Drop

Forward Drop

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E2: Weak dominance

?Blue GreenSource Dest

?

'( , ) ( , ),i i i i i i i iu s s u s s s S

Weak dominance: strictly better strategy for at least one opponent strategy

with strict inequality for at least one s-i

Iterative weak dominance (1-c, 1-c) (-c, 0)

(0, 0) (0, 0)

Blue

Green

Forward

Drop

Forward Drop

BUT

The result of the iterative weak dominance is not unique in general !

Strategy s’i is weakly dominated by strategy si if

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Nash equilibrium (1/2)

Nash Equilibrium: no player can increase its utility by deviating unilaterally

(1-c, 1-c) (-c, 1)

(1, -c) (0, 0)

BlueGreen

Forward

Drop

Forward DropE1: The Forwarder’s Dilemma

E2: The Joint Packet Forwarding game (1-c, 1-c) (-c, 0)

(0, 0) (0, 0)

BlueGreen

Forward

Drop

Forward Drop

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Nash equilibrium (2/2)

* * *( , ) ( , ),i i i i i i i iu s s u s s s S

iu Ui is S

where: utility function of player i

strategy of player i

( ) arg max ( , )i i

i i i i is S

b s u s s

The best response of player i to the profile of strategies s-i is a strategy si such that:

Nash Equilibrium = Mutual best responses

Caution! Many games have more than one Nash equilibrium

Strategy profile s* constitutes a Nash equilibrium if, for each player i,

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Example 3: The Multiple Access game

Reward for successfultransmission: 1

Cost of transmission: c(0 < c << 1)

There is no strictly dominating strategy

(0, 0) (0, 1-c)

(1-c, 0) (-c, -c)

BlueGreen

Quiet

Transmit

Quiet Transmit

There are two Nash equilibria

Time-division channel

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E3: Mixed strategy Nash equilibrium

objectives– Blue: choose p to maximize ublue

– Green: choose q to maximize ugreen

(1 )(1 ) (1 )blueu p q c pqc p c q (1 )greenu q c p

1 , 1p c q c

p: probability of transmit for Blue

q: probability of transmit for Green

is a Nash equilibrium

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Example 4: The Jamming game

transmitter:• reward for successfultransmission: 1• loss for jammed transmission: -1

jammer:• reward for successfuljamming: 1• loss for missed jamming: -1

There is no pure-strategy Nash equilibrium

two channels: C1 and C2

(-1, 1) (1, -1)

(1, -1) (-1, 1)

BlueGreen

C1

C2

C1 C2

transmitter

jammer

1 1,

2 2p q is a Nash equilibrium

p: probability of transmit on C1 for Blue

q: probability of transmit on C1 for Green

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Theorem by Nash, 1950

Theorem: Every finite strategic-form game has a mixed-strategy Nash equilibrium.

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Efficiency of Nash equilibria

E2: The Joint Packet Forwarding game

(1-c, 1-c) (-c, 0)

(0, 0) (0, 0)

BlueGreen

Forward

Drop

Forward Drop

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.

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How to study Nash equilibria ?

Properties of Nash equilibria to investigate:• existence• uniqueness• efficiency (Pareto-optimality)• emergence (dynamic games, agreements)

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Repeated games

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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)

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Strategies in the repeated game

• usually, history-1 strategies, based on different inputs:

– others’ behavior:

– others’ and own behavior:

– utility:

1i i im t s m t 1 ,i i i im t s m t m t

1i i im t s u 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

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The Repeated Forwarder’s Dilemma

(1-c, 1-c) (-c, 1)

(1, -c) (0, 0)

BlueGreen

Forward

Drop

Forward Drop

?

?

Blue Green

stage payoff

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Analysis of the Repeated Forwarder’s Dilemma

Blue strategy Green strategy

AllD AllD

AllD TFT

AllD AllC

AllC AllC

AllC TFT

TFT TFT

infinite game with discounting: 0

ti i

t

u u t

Blue utility Green utility

0 0

1 -c

1/(1-ω) -c/(1-ω)

(1-c)/(1-ω) (1-c)/(1-ω)

(1-c)/(1-ω) (1-c)/(1-ω)

(1-c)/(1-ω) (1-c)/(1-ω)

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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

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http://secowinet.epfl.ch

For the tutorial on game theory:M. Felegyhazi and J.-P. Hubaux, Game Theory in Wireless Networks: A Tutorial Technical report – 2006 [LCA-REPORT-2006-002]

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Book structure

1. Existing networks

2. Upcoming networks

3. Trust

4. Naming and addressing

5. Security associations

6. Secure neighbor discovery

7. Secure routing

8. Privacy protection

9. Selfishness at MAC layer

10. Selfishness in PKT FWing

11. Operators in shared spectrum

12. Behavior enforcement

Appendix A:Security and crypto

Appendix B:Game theory

Security Cooperation

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Who is malicious? Who is selfish?

There is no watertight boundary between malice and selfishness Both security and game theory approaches can be useful

There is no watertight boundary between malice and selfishness Both security and game theory approaches can be useful

Harm everyone: viruses,…

Selective harm: DoS,… Spammer

Cyber-gangster:phishing attacks,trojan horses,…

Big brother

Greedy operator

Selfish mobile station

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From discrete to continuous

Warfare-inspired Manichaeism:

The more subtle case of commercial applications:

Bad guys (they)Attacker

Good guys (we)System (or country) to be defended

0 1

Undesirablebehavior

Desirablebehavior

0 1

• Security often needs incentives• Incentives usually must be secured

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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

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List of Contributors

Aachen University, GermanyAIST, JapanBudapest University of Technology and Economics, HungaryCreate-NET, ItalyDoCoMo Euro-Labs, GermanyEPFL, SwitzerlandHarvard University, USAKonica Italia, ItalyKTH, SwedenMIT, USA Motorola Labs, FranceOxford University, UKStevens Institute of Technology, USATechnical University of Catalonia, SpainTechnical University of Denmark, DenmarkUniversität Duisburg Essen, GermanyUniversität Karlsruhe, GermanyUniversity of Aalborg, DenmarkUniversity of Bologna, ItalyUniversity of California at Berkeley, USAUniversity of California, San Diego, USAUniversity of Dresden, GermanyUniversity of Paderborn, GermanyUniversity of Padova, ItalyUniversity of Piraeus, GreeceVTT, FinlandWINLAB and Rutgers University, USA

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Spectrum Sharing Games in Unlicensed Band Licensed Band

Cellular Operators

• WAN-WiFi competition/cooperation (University of Texas at Austin)

• Cellular operators near national borders (EPFL)• Cellular operators in shared spectrum (EPFL)

Unlicensed BandDevices

• Heterogeneous wireless systems (University of California at Berkeley)

• Wifi Operators (Bell LAB, MIT)

Cognitive Radios

• Opportunistic spectrum sharing (UCSB)• Auction based spectrum sharing (Northwestern)

• Multi-Cell OFDM spectrum sharing (University of Maryland)

3. Spectrum sharing games

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3.1 Spectrum Sharing Games of Network Operators

1. A. Zemlianov and G. de Veciana, “Cooperation and Decision Making in Wireless Multi-provider Setting,” INFOCOM 2005

2. M. Felegyhazi et al., “Border Games in Cellular Networks,” INFOCOM 2007

3. M. Felegyhazi and J.-P. Hubaux, “Wireless Operators in a Shared Spectrum,” INFOCOM 2006

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3.1.1 WAN-WiFi competition/cooperation (University of Texas at Austin)

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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 APcw: cost of switching to a WAN APt: decision time

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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

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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

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• 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)pilotpG

where: – pilot processing gain

– 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

– set of users attached to BS A

0

pilotp A Avpilot

Av pilot pilotown other

G P dSINR

N W I I

Signal-to-interference-plus-noise ratio:

A

pilotown Av Aw

w

I d T

M

B

pilotother Bv B Bw

w

I d P T

M

Own-cell interference

Other-to-own-cell interference

pilotpG

APAvd

AwT

AM

Border games of cellular operators

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Results (1): Incentives for operators to be strategic

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Results (2): Existence of a unique maximum payoff when both operators are strategic

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• Unique and Pareto-optimal Nash equilibrium• Higher pilot power than in the standard Ps = 2W• 10 users in total

standard

Nash equilibrium

Results (3): Best response calculation for two players

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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 behaviorC* - cost for higher pilot power

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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

• devices have omnidirectional antennas

2

2A B MINr r R d

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System model

• A set of users uniformly distributed in the area• Free roaming• Users attach to the base station with the best pilot

signal

• Operators want to cover the largest area with their pilot signal

0

maxi

i iu

Pj ju

j

P g

N P g

2

1iu

iu

gd

where the channel gain:

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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

i i i iU O Y

where γi is the cooperation parameter of player i:• cooperativeness• agreement• power price

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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

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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

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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

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Panel at Mobicom 2007(Montreal, September 13)

Bonobos Vs Chimps: Cooperative and Non-Cooperative

Behavior in Wireless NetworksPanelists:

Jean-Pierre Hubaux, EPFL (organizer and moderator)

Ramesh Johari, Stanford University

P. R. Kumar, UIUC

Joseph Mitola, MITRE Corp.

Heather Zheng, UCSB

BonoboChimpanzeewww.ncbi.nlm.nih.gov www.bio.davidson.edu

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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