Equilibria for Networks with Malicious Users

We consider the problem of characterizing user equilibria and optimal solutions for selfish routing in a given network. We extend the known models by considering malicious behaviour. While selfish users follow a strategy that minimizes their individual cost, a malicious user will use his flow through the network in an effort to cause the maximum possible damage to this cost. We define a generalized model, present characterizations of flows at Wardrop equilibrium and prove bounds for the ratio of the social cost of a flow at Wardrop equilibrium over the cost when centralized coordination among users is allowed.