Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for...
-
Upload
noah-harris -
Category
Documents
-
view
217 -
download
3
Transcript of Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for...
![Page 1: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/1.jpg)
Vaggelis G. Douros Stavros Toumpis
George C. Polyzos
On the Nash Equilibria of Graphical Games for Channel Access
in Multihop Wireless Networks
1
WWRF-WCNC @ Istanbul, 06.04.2014
![Page 2: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/2.jpg)
Motivation (1)
New communication paradigms will arise
2
![Page 3: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/3.jpg)
Motivation (2)
Proximal communication-D2D scenarios More devices…more interference Our work: Channel access in such scenarios which
device should transmit/receive data and when3
![Page 4: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/4.jpg)
Problem Description (1)
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
4
2 3 541 6
2 3 541 6
![Page 5: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/5.jpg)
Problem Description (2)
The problem: How can these autonomous nodes avoid collisions?
The (well-known) solution: maximal scheduling…
is not enough/incentive-compatible
We need to find equilibria!
5
2 31
2 31
2 31
![Page 6: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/6.jpg)
On the Nash Equilibria (1)
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
6
21
21
21
21
![Page 7: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/7.jpg)
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
![Page 8: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/8.jpg)
On the Nash Equilibria (3)
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 Wait8
2 3 541
2 3 541
2 3 541
2 3 541
This is a NE!
![Page 9: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/9.jpg)
Performance Evaluation (1)
Perfect k-ary trees of depth d Average number of rounds for
convergence to a NE as a function of – k and d – the number of nodes
Analysis of the avg./max./min. number of successful transmissions at a NE
9
![Page 10: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/10.jpg)
Performance Evaluation (2)
Fast convergence, ~ proportional with the logarithm of the number of nodes
Effect of the depth d more important than param. k
10
![Page 11: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/11.jpg)
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
11
Longer
Shorter
![Page 12: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/12.jpg)
Take-home Messages
Channel access for selfish devices in proximity can lead to efficient NE with minimal cooperation– stronger notion than maximal scheduling– fast convergence– without spending much energy
More (sophisticated) schemes & tradeoffs, theoretical analysis etc. @IWCMC 2014
12
![Page 13: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/13.jpg)
Acknowledgement (1)
Vaggelis G. Douros is supported by the HERAKLEITOS II Programme which is co-financed by the European Social Fund and National Funds through the Greek Ministry of Education.
13
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 I I . I nvesting in knowledge society through the European Social Fund.
![Page 14: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/14.jpg)
Acknowledgement (2)
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.
14
![Page 15: Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 WWRF-WCNC.](https://reader035.fdocuments.in/reader035/viewer/2022062801/56649e525503460f94b47b8c/html5/thumbnails/15.jpg)
Teşekkür Ederim!
Vaggelis G. Douros
Mobile Multimedia Laboratory
Department of Informatics
Athens University of Economics and Business
http://mm.aueb.gr/~douros
15