Research at Virginia Tech Into the Application of Game Theory to Wireless Networks

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Research at Virginia Tech Into the Application of
Game Theory to Wireless Networks

• James Neel
• April 2, 2004

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Game Theory Group

• Studying application of game theory to
  distributed radio resource management
• Sponsors
• ONR, Motorola, IREAN

• Focus areas
• Power control, Interference avoidance, Adaptive
  MAC algorithms, Network formation, Node
  participation
• Meetings Wednesdays 400 in Durham 432
• More information available on website
• http//www.mprg.org/people/gametheory/index.shtml

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Game Theory Group

• Professors
• Jeffrey H. Reed
• Robert P. Gilles
• Luiz A. DaSilva
• Allen B. MacKenzie
• Annamalai Annamalai
• R. Michael Beuhrer
• Students
• James Neel
• Vivek Srivastava
• Samir Ginde
• Kevin Lau
• Rekha Menon
• James Hicks (got a job)

• Exploring application of game theory to wireless
  networks in the following areas
• Physical layer adaptations
• Distributed power control
• Distributed waveform adaptations
• Node participation (resource sharing)
• Network formation
• Adaptive MAC strategies

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Presentation overview

• What is game theory?
• The application of game theory to wireless
  networks
• Example applications and results

?
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What is game theory?

• What is a game?

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Is this a game?
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Is this a game?
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Is this a game?
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Is this a game?

• When is it a game?

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What is a game?

• A game is an interactive decision problem
• Game Theory is a part of (applied) mathematics
  that describes and studies interactive decision
  problems

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Basic game theory models

• Normal form game
• Extensive form game
• Repeated game

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Normal form game
Components

• A set of 2 or more players
• A set of actions for each player
• A set of utility functions that describe the
  players preferences over the action space

Player 1 Actions a, b Player 2 Actions A, B
States from which no player can unilaterally
deviate and improve are Nash Equilibriums
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Extensive form games
Components

• A set of players.
• The actions available to each player at each
  decision moment (state).
• A way of deciding who is the current decision
  maker.
• Outcomes on the sequence of actions.
• Preferences over all outcomes.

1
1
C
Example of backwards induction
2,4
4,6
3,1
0,2
5,3
S
S
1,0
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Repeated game

• A stage game (normal form game) is played
  repeatedly with payoffs after each stage
• Game can continue indefinitely (infinite horizon)
  or end at a specified time (finite horizon)
• Players may consider future payoffs when playing
  and may consider when future payoffs will occur

Example stage game
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Comments on play in repeated games

• Myopic Processes
• Players have no knowledge about utility
  functions, or expectations about future play,
  typically can observe or infer current actions
• Best response dynamic maximize individual
  performance presuming other players actions are
  fixed
• Better response dynamic improve individual
  performance presuming other players actions are
  fixed

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Better response dynamic

• During each stage game, player(s) choose an
  action that increases their payoff, presuming
  other players actions are fixed

B
A
a
1,-1
0,2
b
-1,1
2,2
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Best response dynamic

• During each stage game, player(s) choose the
  action that maximizes their payoff, presuming
  other players actions are fixed

B
A
C
a
-1,1
1,-1
0,2
b
1,-1
-1,1
1,2
c
2,1
2,0
2,2
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Repeated game communication

• Players agree to play in a certain manner
• Threats can force play to almost any state
• Breaks down with finite horizon

C
N
Nada
-5,5
0,0
nada
-100,0
c
-1,1
5,-5
-100,-1
-100,-100
n
-1,-100
0,-100
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Potential games

• How to identify
• Or find an ordinal transformation
• Key properties
• Nash equilibrium exists
• Better response dynamic converges
• Why we care
• Steady state exists
• Virtually every decision updating process
  converges (no communication required)
• Once modeled, steady states easy to identify
  (potential function maximizers)

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Supermodular games

• How to identify
• Key properties
• Best response dynamic converges
• Nash equilibrium generally exists
• Why we care
• Most decision updating processes converge
• (no communication required)

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Application of Game Theory to Wireless Networks
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Modeling a network as a game
Network
Game
Nodes
Players
Adaptations
Actions
Algorithms
Utility Functions Learning
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Conditions for applying game theory to RRM

• Conditions for rationality
• Well defined decision making processes
• Expectation of how changes impacts performance
• Conditions for a nontrivial game
• Multiple interactive decision makers
• Nonsingleton action sets
• Conditions generally satisfied by distributed
  dynamic RRM schemes

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Example application appropriateness

• Inappropriate applications
• Cellular Downlink power control (single cell)
• Site Planning
• Appropriate applications
• Distributed power control on non-orthogonal
  waveforms
• Ad-hoc power control
• Cell breathing
• Adaptive MAC
• Network formation (localized objectives)

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Analyzing distributed dynamic behavior

• Dynamic benefits
• Improved spectrum utilization
• Improve QoS
• Many decisions may have to be localized
• Distributed behavior
• Adaptations of one radio can impact adaptations
  of others
• Interactive decisions
• Difficult to predict performance

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Key issues

• Steady state existence
• Steady state optimality
• Convergence
• Stability
• Scalability

Convergence How do initial conditions impact
the system steady state? What processes will
lead to steady state conditions? How long
does it take to reach the steady state?
Steady State Existence Is it possible to
predict behavior in the system? How many
different outcomes are possible?
Optimality Are these outcomes desirable?
Do these outcomes maximize the system target
parameters?
Stability How does system variations impact
the system? Do the steady states change?
Is convergence affected?
Scalability As the number of devices
increases, How is the system impacted?
Do previously optimal steady states remain
optimal?
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Example Applicationsand Results
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Power control game model
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Example power control game

• Parameters
• Single cluster (single node of interest)
• DS-SS multiple access
• Pi Pj 0, Pmax ? i,j ?N
• Utility target BER
• Preference preserving transformation

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Information provided by game theory

• The following is a sufficient condition to show
  that the game is a potential game
• Note that
• Thus we know the following
• Steady state exists
• Network converges by better response to
  steady-state
• Minimal network implementation complexity
  Neel04
• Network steady state is given by maximizer of

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Snapshot inner outer loop power control

• Parameters
• Single Cluster
• DS-SS multiple access
• Pi Pj 0, Pmax ? i,j ?N
• Utility target SINR
• Supermodular best response convergence

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Other interesting results

• The following single cluster algorithms are also
  potential games
• Target SINR, Target QoS, Target throughput
• The following multi-cluster algorithms are
  supermodular games
• Target BER, Target SINR,
• Target throughput, Target QoS
• Furthermore holds even if different nodes have
  different target QoS
• For these multi-cluster algorithms we know
• Steady state exists
• Network converges by best response to steady-state

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Adaptive interference results

• Radios adapt waveform (modulation, frequency,
  spreading code) to minimize impact of
  interfering signals
• Received Signal Model

J. E. Hicks, A. B. MacKenzie, J. Neel, J. H.
Reed, A Game Theory Perspective on Interference
Avoidance Submitted to Globecom04
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Following are all potential games

• SINR/Corr Games
• SINR measured at output of correlation receiver
• MSE Games
• MSE measured at output of correlation receiver

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Following are all potential games

• 2 player SINR/MSINR game
• SINR measured at output of MSINR receiver
• 2 player MSE/MSINR game
• MSE measured at output of MSINR receiver

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Summary

• Game theory can be applied to wireless networks
  with distributed decision making processes
• Demonstration of model applicability can be used
  to solve for steady states, establish convergence
• Currently refining models to establish stablility

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Game Theory Group

• Studying application of game theory to
  distributed radio resource management
• Sponsors
• ONR, Motorola, IREAN

• Focus areas
• Power control, Interference avoidance, Adaptive
  MAC algorithms, Network formation, Node
  participation
• Meetings Wednesdays 400 in Durham 432
• More information available on website
• http//www.mprg.org/people/gametheory/index.shtml