Manuel Rode

Nashification and the coordination ratio for a selfish routing game

We study the problem of n users selfishly routing traffic through a network consisting of m parallel related links. Users route their traffic by choosing private probability distributions over the links with the aim of minimizing their private latency. In such an environment Nash equilibria represent stable states of the system: no user can improve its private latency by unilaterally changing its strategy. Nashification is the problem of converting any given non-equilibrium routing into a Nash equilibrium without increasing the social cost. Our first result is an O(nm2) time algorithm for Nashification. This algorithm can be used in combination with any approximation algorithm for the routing problem to compute a Nash equilibrium of the same quality. In particular, this approach yields a PTAS for the computation of a best Nash equilibrium. Furthermore, we prove a lower bound of Ω(2√n) and an upper bound of O(2n) for the number of greedy selfish steps for identical link capacities in the worst case. In the second part of the paper we introduce a new structural parameter which allows us to slightly improve the upper bound on the coordination ratio for pure Nash equilibria in [3]. The new bound holds for the individual coordination ratio and is asymptotically tight. Additionally, we prove that the known upper bound of 1+√4m-3/2 on the coordination ratio for pure Nash equilibria also holds for the individual coordination ratio in case of mixed Nash equilibria, and we determine the range of m for which this bound is tight.

A New Model for Selfish Routing

In this work, we introduce and study a new model for selfish routing over non-cooperative networks that combines features from the two such best studied models, namely the KP model and the Wardrop model in an interesting way.

Selfish Routing in Non-cooperative Networks: A Survey

We study the problem of n users selfishly routing traffics through a shared network. Users route their traffics by choosing a path from their source to their destination of the traffic with the aim of minimizing their private latency. In such an environment Nash equilibria represent stable states of the system: no user can improve its private latency by unilaterally changing its strategy.

Which Is the Worst-Case Nash Equilibrium?

A Nash equilibrium of a routing network represents a stable state of the network where no user finds it beneficial to unilaterally deviate from its routing strategy. In this work, we investigate the structure of such equilibria within the context of a certain game that models selfish routing for a set of n users each shipping its traffic over a network consisting of m parallel links. In particular, we are interested in identifying the worst-case Nash equilibrium – the one that maximizes social cost. Worst-case Nash equilibria were first introduced and studied in the pioneering work of Koutsoupias and Papadimitriou [9].

On the Problem of Scheduling Flows on Distributed Networks

We consider the problem of scheduling a given flow on a synchronous distributed network. This problem arises using diffusion-based approaches to compute a balancing flow, which has to be scheduled afterwards. We show that every distributed scheduling strategy requires at least 3/2 times the minimum number of rounds. Furthermore we give a distributed algorithm for flows on tree networks, which requires at most two times the optimal number of rounds.