Vaggelis G. Douros Stavros Toumpis George C. Polyzos On the Nash Equilibria of Graphical Games for Channel Access in Multihop Wireless Networks 1 Istanbul,

Motivation (1) New communication paradigms will arise 2

Motivation (2) Proximal communication-D2D scenarios More devices…more interference Our work: Channel access in such scenarios  which device should transmit/receive data and when 3

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

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!

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

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) 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 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 – k and d – the number of nodes Analysis of the avg./max./min. number of successful transmissions at a NE 9

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

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

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

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

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

Teşekkür Ederim! Vaggelis G. Douros Mobile Multimedia Laboratory Department of Informatics Athens University of Economics and Business 15