Competitive routing in multiuser communication networks
IEEE/ACM Transactions on Networking (TON)
Journal of the ACM (JACM)
A survey on networking games in telecommunications
Computers and Operations Research
Learning in the presence of noise
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
Convergence of population dynamics in symmetric routing games with a finite number of players
GameNets'09 Proceedings of the First ICST international conference on Game Theory for Networks
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
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We study the traffic routing problem in networks whose agents try to minimize their latencies by employing a distributed learning rule inspired by the replicator dynamics of evolutionary game theory. The stable states of these dynamics coincide with the network's (Wardrop) equilibrium points and we find that they form a convex polytope whose dimension is determined by the network's degeneracy index (an important concept which measures the overlap of the agents' paths). Still, despite this abundance of stable states, we find that (almost) every solution trajectory converges to an equilibrium point at an exponential rate. On the other hand, a major challenge occurs when network latencies fluctuate unpredictably due to random exogenous factors. In that case, we show that the time-average of the traffic flows of sufficiently patient agents is still concentrated in a neighborhood of evolutionarily stable equilibria and we estimate analytically the corresponding stationary distribution and convergence times.