Mixed Equilibrium for Multiclass Routing Games

We consider a network shared by noncooperative two types of users, group users and individual users, each user of the first type has a significant impact on the load of the network, whereas a user of the second type doesn’t. Both group users as well as individual users choose their routes so as to minimize their costs. We further consider the case that the users may have side constraints. We study the concept of mixed equilibrium (mixing of Nash equilibrium and Wardrop equilibrium). We establish its existence and some conditions for its uniqueness. Then we apply the mixed equilibrium to a parallel links network and to a case of load balancing. Keywords—Game Theory, routing, networks, Nash equilibrium, Wardrop equilibrium, mixed-equilibrium, side constraints.