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Non-Cooperative Behavior in Wireless Networks
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Transcript of Non-Cooperative Behavior in Wireless Networks
Non-Cooperative Behavior
in Wireless Networks
Márk Félegyházi (EPFL)PhD. public defense
July 9, 2007
July 9, 2007 Márk Félegyházi (EPFL) 2
Summary of my research
► 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
Part I: Introduction to game theory
July 9, 2007 Márk Félegyházi (EPFL) 3
Multi-Radio Channel Allocation Problem
► C orthogonal channels► N communicating pairs of devices► k radios at each device
,i xknumber of radios
by sender i on channel x
→
,i i xx C
k k
,x i xi N
k k
, ( )i i i x xx C
u k k
Nash equilibrium: No player has an incentive to unilaterally deviate.
* * *( , ) ( , ),i i i i i i iu s s u s s s S
Proposition: If S* is a NE in GMRCA, then dy,x ≤ 1, for any channel x and y.
► blabla, ► blabla, blabla
How to Share a Pie with Selfish Researchers
Márk Félegyházi (EPFL)PhD. public defense
July 9, 2007
Who Know Game Theory
July 9, 2007 Márk Félegyházi (EPFL) 6
Motivation
► 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
BEFORE
NOW
What is the effect of selfish behavior in pie sharing?
July 9, 2007 Márk Félegyházi (EPFL) 7
System model
► C pies► N selfish and rational (= hungry)
researchers► k plates for each researcher
SYSTEM:
► 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
ASSUMPTIONS:
July 9, 2007 Márk Félegyházi (EPFL) 8
total number of plates by researcher i
number of plates by researcher i at pie x
Example
► C = 6 pies► N = 4 hungry researchers► k = 4 plates for each researcher
,i xk
,i i xx C
k k
,x i xi N
k k
total number of plates demanding pie
x
July 9, 2007 Márk Félegyházi (EPFL) 9
The pie-cut functions► pies have all the same size and quality ► π t(kx) – total size of the shares of any pie x
► π(kx) – size of a share per plate
33
July 9, 2007 Márk Félegyházi (EPFL) 10
Dining Game Theoreticians (DGT) game
► selfish (=hungry) researchers► non-cooperative game GDGT
– players → researchers– strategy → plate allocation – payoff → total amount of cookie
► payoff:
, ( )i i i x xx C
u k k
(3) (4) 2 (4)Maxim iu
July 9, 2007 Márk Félegyházi (EPFL) 11
Stability: Nash equilibrium
Nash equilibrium: No researcher changes if the others keep their plates.
Best response: Best strategy of a researcher given the strategies of others.
July 9, 2007 Márk Félegyházi (EPFL) 13
Recognition: In a stable state (NE), dy,x ≤ 1 for any two pies x and y.
Cut the pies in (almost) the same number of pieces
x
► pick two pies x and y, where kx ≥ ky► demand: dx,y = kx – ky
y
July 9, 2007 Márk Félegyházi (EPFL) 14
Distribute your plates
Truth 1: The researchers won’t change the position of their plates (NE), if:
► dx,y ≤ 1 and
► ki,x ≤ 1.
Nash Equilibrium:
► pick two pies x and y, where kx ≥ ky► demand: dx,y = kx – ky
Put 1 plate per pie
July 9, 2007 Márk Félegyházi (EPFL) 15
Put more plates to some pies
Truth 2: The researchers won’t change the position of their plates (NE), if: ► dx,y ≤ 1,
► for any researcher i who has ki,x ≥ 2, x in C,
► for any researcher i who has ki,x ≥ 2 and x in C+, ki,y ≥ ki,x – 1, for all y in C–
,
( 1) ( 1)
( 1) ( )x x
i xx x
k kk
k k
► pick two pies x and y, where kx ≥ ky► demand: dx,y = kx – ky► more and less demanded pies C+ and C–
Nash Equilibrium:
Put more platesto some pies
July 9, 2007 Márk Félegyházi (EPFL) 16
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
July 9, 2007 Márk Félegyházi (EPFL) 17
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
July 9, 2007 Márk Félegyházi (EPFL) 18
Back to wireless networking
► C orthogonal channels – C pies► N communicating pairs of devices – N researchers► k radios at each device – k plates