Properties of equilibria in competitive routing with several user types

In recent years there has been a growing interest in models for routing in networks in which decisions are taken in a non-cooperative way. Instead of a single decision maker, one considers a number of decision makers having each its own utility to maximize by routing its own flow. This gives rise to a non-cooperative game whose solution concept is the Nash equilibrium. In the special case where each decision maker wishes to find a minimal path for each routed job (a packet) then the solution concept is the Wardrop equilibrium. It is well known that equilibria may exhibit inefficiencies and paradoxical behavior, such as the famous Braess paradox in which the addition of a link to a network results in worse performance to all users. This raises the challenge of how to upgrade the network so that it indeed results in improved performance. We present guidelines for the allocation of extra resources in a manner that Braess' paradox is avoided, and the performance of every user is improved.