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Non-Cooperative Behavior in Wireless Networks. Márk Félegyházi (EPFL) PhD. public defense. July 9, 2007. Summary of my research. Part I: Introduction to game theory. Ch 1: A tutorial on game theory Ch. 2: Multi-radio channel allocation in wireless networks

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non cooperative behavior in wireless networks

Non-Cooperative Behavior in Wireless Networks

Márk Félegyházi (EPFL)

PhD. public defense

July 9, 2007

summary of my research
Summary of my research

Part I:

Introduction to game theory

  • Ch 1: A tutorial on game theory
  • Ch. 2: Multi-radio channel allocation in wireless networks
  • Ch. 3: Packet forwarding in static ad-hoc networks
  • Ch. 4: Packet forwarding in dynamic ad-hoc networks
  • Ch. 5: Packet forwarding in multi-domain sensor networks
  • Ch. 6: Cellular operators in a shared spectrum
  • Ch. 7: Border games in cellular networks

Part II:

Non-cooperative users

Part III:

Non-cooperative network operators

Márk Félegyházi (EPFL)

multi radio channel allocation problem
Multi-Radio Channel Allocation Problem

number of radios by sender i

on channel x

  • C orthogonal channels
  • N communicating pairs of devices
  • k radios at each device

Nash equilibrium: No player has an incentive to unilaterally deviate.

Proposition: If S* is a NE in GMRCA, then dy,x≤ 1, for any channel x and y.

  • blabla,
  • blabla, blabla

Márk Félegyházi (EPFL)

how to share a pie with selfish researchers

How to Share a Pie with Selfish Researchers

Who Know Game Theory

Márk Félegyházi (EPFL)

PhD. public defense

July 9, 2007

problem
Problem

Dining

Game Theoreticians

Márk Félegyházi (EPFL)

motivation
Motivation

BEFORE

  • pies were controlled by a trusted central authority
    • “Mark, I would strongly encourage you share the pie with Panos”
  • it was difficult to get enough plates

  • no central control how to cut the pies
  • it is easy to get more plates to get a bigger share

NOW

What is the effect of selfish behavior in pie sharing?

Márk Félegyházi (EPFL)

system model
System model

SYSTEM:

  • C pies
  • N selfish and rational (= hungry) researchers
  • k plates for each researcher

ASSUMPTIONS:

  • the central authority does not help to share the pies
  • pies have the same size and quality (strawberry)
  • each researcher can reach any pie (by allocating a plate there)
  • pies are fairly shared
  • one slice on one plate

Márk Félegyházi (EPFL)

example
Example
  • C = 6 pies
  • N = 4 hungry researchers
  • k = 4 plates for each researcher

number of plates by researcher i at pie x

total number of plates by researcheri

total number of plates demanding pie x

Márk Félegyházi (EPFL)

the pie cut functions
The pie-cut functions
  • pies have all the same size and quality
  • πt(kx)– total size of the shares of any pie x
  • π(kx) – size of a share per plate

3

3

Márk Félegyházi (EPFL)

dining game theoreticians dgt game
Dining Game Theoreticians (DGT) game

selfish (=hungry) researchers

non-cooperative game GDGT

players→ researchers

strategy → plate allocation

payoff → total amount of cookie

payoff:

Márk Félegyházi (EPFL)

stability nash equilibrium
Stability: Nash equilibrium

Best response: Best strategy of a researcher given the strategies of others.

Nash equilibrium: No researcher changes if the others keep their plates.

Márk Félegyházi (EPFL)

the question
The Question

Where shall I put my plates?

Márk Félegyházi (EPFL)

cut the pies in almost the same number of pieces
Cut the pies in (almost) the same number of pieces

pick two pies x and y, where kx ≥ ky

demand: dx,y = kx – ky

Recognition: In a stable state (NE), dy,x≤ 1 for any two pies x and y.

Márk Félegyházi (EPFL)

distribute your plates
Distribute your plates
  • pick two pies x and y, where kx ≥ ky
  • demand: dx,y = kx – ky

Truth 1: The researchers won’t change the position of their plates (NE), if:

  • dx,y≤ 1and
  • ki,x≤ 1.

Nash Equilibrium:

Put 1 plate per pie

Márk Félegyházi (EPFL)

put more plates to some pies
Put more plates to some pies
  • pick two pies x and y, where kx ≥ ky
  • demand: dx,y = kx – ky
  • more and less demanded pies C+ and C–

Truth 2:The researchers won’t change the position of their plates (NE), if:

  • dx,y≤ 1,
  • for any researcher i who haski,x≥ 2, x in C,
  • for any researcher i who haski,x≥ 2 and x inC+, ki,y≥ ki,x– 1, for all y inC–

Nash Equilibrium:

Put more plates

to some pies

Márk Félegyházi (EPFL)

convergence to stable states
Convergence to stable states

Algorithm with imperfect info:

  • researchers don’t know the demand for pies they are not demanding themselves
  • move plates from demanded pies to other randomly chosen pies
  • desynchronize the changes
  • convergence is not ensured

Márk Félegyházi (EPFL)

summary
Summary
  • hungry researchers having several plates
  • Dining Game Theoreticians game
  • results for a stable pie sharing (NE):
    • researchers should use all their plates
    • similar demand for each pie
    • two types of stable states
    • NE are efficient both in theory and practice
  • fairness issues
  • equilibria for coalitions
  • algorithms to achieve efficient NE:
    • centralized algorithm with perfect information
    • distributed algorithm with imperfect information

Márk Félegyházi (EPFL)

back to wireless networking
Back to wireless networking
  • C orthogonal channels – C pies
  • N communicating pairs of devices – N researchers
  • k radios at each device – k plates

Márk Félegyházi (EPFL)

some contributions
Some contributions
  • Stability and convergence of multi-radio channel allocation in wireless networks
  • Cooperation conditions for packet forwarding in ad hoc networks
  • Spectrum sharing strategies of wireless network (cellular) operators

Márk Félegyházi (EPFL)