Existence of Nash Equilibria in Selfish Routing Problems

The problem of routing traffic through a congested network is studied. The framework is that introduced by Koutsoupias and Papadimitriou where the network is constituted by m parallel links, each having a finite capacity, and there are n selfish (noncooperative) agents wishing to route their traffic through one of these links: thus the problem sets naturally in the context of noncooperative games. Given the lack of coordination among the agents in large networks, much effort has been lavished in the framework of mixed Nash equilibria where the agent's routing choices are regulated by probability distributions, one for each agent, which let the system reach thus a stochastic steady state from which no agent is willing to unilaterally deviate. Recently Mavronicolas and Spirakis have investigated fully mixed equilibria, where agents have all non zero probabilities to route their traffics on the links. In this work we concentrate on constrained situations where some agents are forbidd...

• Type: Conference
• Year: 2004
• Where: SIROCCO
• Authors: Alessandro Ferrante, Mimmo Parente
• Keywords: Agent's Routing Choices, Mixed Nash Equilibria, Probability Distributions, SIROCCO 2004, SIROCCO 2007