On the Nash Equilibria of Graphical
Games for Channel Access
in Multihop Wireless Networks
Vaggelis G. Douros
Stavros Toumpis
George C. Polyzos
WWRF-WCNC @
Istanbul, 06.04.2014
1
Motivation (1)

2
New communication paradigms will arise
Motivation (2)



3
Proximal communication-D2D scenarios
More devices…more interference
Our work: Channel access in such scenarios 
which device should transmit/receive data and when
Problem Description (1)



4
1
2
3
4
5
6
1
2
3
4
5
6
Each node either transmits to one of its neighbors or
waits
Node 3 transmits successfully to node 4 IFF none of
the red transmissions take place
If node 3 decides to transmit to node 4, then none of
the green transmissions will succeed
Problem Description (2)




5
The problem: How can these
autonomous nodes avoid
collisions?
The (well-known) solution:
maximal scheduling…
is not enough/incentivecompatible 
We need to find equilibria!
1
2
3
1
2
3
1
2
3
On the Nash Equilibria (1)




6
How can we find a Nash Equilibrium?
The (well-known) solution: Apply a best
response scheme…
will not converge 
Our approach: A distributed iterative
randomized scheme, where nodes
exchange feedback in a 2-hop
neighborhood to decide upon their new
strategy
1
2
1
2
1
2
1
2
On the Nash Equilibria (2)

This is a special type of game called graphical game
Payoff depends on the strategy of nodes that are up
to 2 hops away

c, e: cost transmission/reception (c>e)

7
On the Nash Equilibria (3)



8
Each node i has |Di|
neighbors and |Di|+1
strategies. Each strategy
is chosen with prob.
1/(|Di|+1)
A successful
transmission is repeated
in the next round
Strategies that cannot be
chosen increase the
probability of Wait
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
This is a NE! 
Performance Evaluation (1)


Perfect k-ary trees of depth d
Average number of rounds for
convergence to a NE as a
function of
–
–

9
k and d
the number of nodes
Analysis of the avg./max./min.
number of successful
transmissions at a NE
Performance Evaluation (2)


10
Fast convergence, ~ proportional with the logarithm
of the number of nodes
Effect of the depth d more important than param. k
Performance Evaluation (3)


For trees of similar number of nodes, longer trees 
more successful transmissions
Any NE is almost equally preferable in terms of
number of successful transmissions
Longer
Shorter
11
Take-home Messages

Channel access for selfish devices in
proximity can lead to efficient NE with
minimal cooperation
–
–
–

12
stronger notion than maximal scheduling
fast convergence
without spending much energy
More (sophisticated) schemes & tradeoffs,
theoretical analysis etc. @IWCMC 2014
Acknowledgement (1)

Vaggelis G. Douros is supported by the
HERAKLEITOS II Programme which is cofinanced by the European Social Fund and
National Funds through the Greek Ministry of
Education.
This research has been co-financed by the European Union
(European Social Fund – ESF) and Greek national funds through
the Operational Program "Education and Lifelong Learning" of
the National Strategic Reference Framework (NSRF) - Research
Funding Program: Heracleitus II. Investing in knowledge
society through the European Social Fund.
13
Acknowledgement (2)

14
The research of Stavros Toumpis has been co-financed
by the European Union (European Social Fund ESF)
and Greek national funds through the Operational
Program “Education and Lifelong Learning” of the
National Strategic Reference Framework (NSRF)
Research Funding Program: THALES. Investing in
knowledge society through the European Social Fund.
 Teşekkür Ederim! 
Vaggelis G. Douros
Mobile Multimedia Laboratory
Department of Informatics
Athens University of Economics and Business
[email protected]
http://mm.aueb.gr/~douros
15