Game Theory and Adaptive Wireless Networks

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Game Theory and Adaptive Wireless Networks

• James Neel
• November 11, 2003
• Reed Student Meeting

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Presentation Overview

• Motivation
• A Little Light Game Theory
• An Example
• Whats Currently Going On

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Analyzing Distributed Adaptive SDR Behavior

• Adaptive SDR Benefits
• Improved Spectrum Utilization
• Improve QoS
• Many decisions may have to be localized
• Distributed Behavior
• Adaptations of one SDR 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? How long does it
take to reach the steady state?
Stability How does system variations impact
the system? Do the steady states change?
Is convergence affected
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?
Scalability As the number of devices
increases, How is the system impacted?
Do previously optimal steady states remain
optimal?
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A Little Light Game Theory
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Game Theory
Used to predict the outcome of interactions of
rational self-interested agents.
In normal form, a game consists of three primary
components
N set of players Ai set of actions available
to player i A space of actions available to the
players ui set of individual objective
functions
Purpose is to identify steady-state conditions
(Nash Equilibrum) from which no player would
rationally choose to alter their action as it
reduces their objective function.
for all bi ?Ai and all i ? N
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Terminology and Key Theory
Best Response Function
Nash Equilibrium
An action tuple a is a NE iff
An equivalent statement A NE is a point a in
action space where the best response functions
map back onto a. Note that this is a fixed
point a BR(a)
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Example Game

• Prisoners Dilemma

a2
b2
a1
1,1
-5,5
b1
-1,-1
5,-5
Just because something is a steady-state, it
doesnt mean that its a good state.
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Game Theory and Wireless Networks
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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
• How to Identify

Find an ordinal transformation for which this
works.
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Model Parameters (1/2)
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Model Parameters (2/2)
Nodes of Interest
Partitioned Nodes of Interest
Single Node of Interest
Unpartitioned Nodes of Interest
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Distributed Power Control Network with Target BER
Scenario
Single Cell, n mobiles, uplink
Pi 0, Pmax
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Quick Derivation
Ordinal Transformation to Target SINR
Satisfies Condition for Ordinal Potential
Game (Note since hgt0, also supermodular)
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Current Game Theory Research Projects

• ONR
• Motorola

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ONR

• Three Areas of Focus
• Physical Layer Adaptations
• Distributed Power Control
• Waveform Adaptations (Interference Avoidance)
• Node Participation
• Network Formation
• Current Participants
• Jeff Reed, James Neel, James Hicks,
• Robert Gilles (Econ)
• Vivek Srivastava (ARI), Luiz DaSilva (ARI)

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Motorola

• Areas of Focus
• Commercial Power Control Schemes
• Adaptive MAC Strategies
• Participants at various points
• Neel, Samir Ginde (Buehrer), Kevin Lau (Annamalai)

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More Information

• All sorts of information (tutorials, papers,
  presentations, surveys) at
• www.mprg.org/people/gametheory/index.shtml
• Game Theory Group Meetings
• Like a mini conference
• Every other Wednesday (Nov 19)
• 400 500 PM
• MPRG Conference Room