Application of Game Theory to Distributed Power Control

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Application of Game Theory to Distributed Power
Control

• James Neel
• janeel_at_vt.edu
• Electrical Engineering
• (Advisor Jeffrey H. Reed)

2004 IREAN Research Workshop
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This presentation examines application of game
theory to distributed power control.
Distributed power control
Key game models
Discoveries
My research applies powerful well-established
game models to distributed power control
algorithms to yield insights into steady-states,
convergence, and stability.
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But first, a little about myself

• Current degree program
• PhD Electrical Engineering
• Spring 2003 Summer 2005
• Prior experience
• MSEE 2002 Virginia Tech
• BSEE 1999 Virginia Tech
• Co-op Nortel Networks 1997, 1998
• Goals
• Finish PhD
• 5-10 years in industry
• Return to academia

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Distributed power control

• Nodes independently adjust power level
  according to an objective function, ui,
  performance metrics, and a power update algorithm
• Makes most sense in ad-hoc environment, however
  adaptations of a single node may lead to network
  wide cascade
• Interactive decision making process makes
  algorithms difficult to analyze
• But convergent behavior is a fundamental
  requirement for any distributed RRM scheme

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Distributed power control

• My research examines the following convergence
  issues for ad-hoc power control algorithms
• Existence of a steady state
• Identification of update algorithms that lead to
  steady state
• Convergence rate
• Approach leverage results and models from game
  theory

• Nodes independently adjust power level
  according to an objective function, ui,
  performance metrics, and a power update algorithm
• Makes most sense in ad-hoc environment, however
  adaptations of a single node may lead to network
  wide cascade
• Interactive decision making process makes
  algorithms difficult to analyze
• But convergent behavior is a fundamental
  requirement for any distributed RRM scheme

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Game theory and wireless networks
Solution of games Nash equilibriums yields
information on networks convergence and steady
states
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Power control game model basics

• Player set N
• Set of decision making radios
• Individual nodes i, j ? N
• Actions
• Pi power levels available to node I
• May be continuous or discrete
• pi power level chosen by player i
• P power space
• p power tuple (vector)
• Nodes of interest
• Each node has a node or set of nodes at which it
  measures performance
• ?i the set of nodes of interest of node i
• Link gain
• hij gain from node i to node j. This can
  include path loss and antenna gain (think link
  budget)
• Most appropriate in narrow band models

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?5
5
?0
2
0
?1
?4
?3
?2
4
3
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Power control game model basics

• Utility functions
• Can be equated to a cognitive radios observation
  valuation
• May be given explicitly, or inferred from
  algorithms preferences
• For instance, consider an algorithm that
  increments transmit power when below a target BER
  and decrements transmit power when above a target
  BER
• From this, an ordered set of preference relations
  can be constructed as follows greatest
  preference given to the power vector that yields
  the target BER, decreasing preference given as a
  function of distance from BER (distance could be
  measured in different ways)
• General form

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Potential games

• Key properties
• Nash equilibrium exists
• Better response (myopic) dynamic converges
• Why we care
• Steady state exists
• Virtually every decision updating process
  converges
• Minimal level of network complexity
• Once modeled, steady states easy to identify
• Modeling conditions

Find an ordinal transformation for which this
works.
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Supermodular games

• Key properties
• Broad conditions for existence of Nash
  equilibriums
• Best response (myopic) dynamic converges
• Why we care
• Easier to establish existence of steady-state
• Many decision updating process converges
• Low level of network complexity
• Modeling conditions

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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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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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Multidisciplinary aspects

• Approach is inherently multidisciplinary
• Applies traditional techniques from economics
  (game theory) to address problem from wireless
  engineering (radio resource management)
• Multidiscipline approach provides
• unique perspectives and insights
• into both disciplines
• Development of analytic framework for distributed
  RRM is leading to refinements to theory of
  potential games

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Status and plans

• Current status
• Third semester PhD student
• Numerous results published
• Some pure game theory results also produced
• Research webpage
• Short term plans
• Extend to random access ad-hoc networks
• Long term plans
• Migrate models to stochastic channels

www.mprg.org/people/gametheory/index.shtml
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Summary

• Game theory can produce valuable information
  about distributed power control
• Steady state existence
• Convergence
• The use of models can significantly reduce
  analysis complexity
• Potential games
• Supermodular games

Questions?