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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 does not. 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.

We consider competitive routing in multicast networks from a noncooperative game theoretical perspective. There are N users sharing a network, and each has to send a quantity of packets to a different set of addressees (each address must receive the same packets). To do this the user has only to send one copy of a packet, the network making the duplications of the packets at appropriate nodes (depending on the chosen trees). The routing choice of a user is how to split its flow between different multicast trees. We present different criteria for optimization of this type of game. We treat two specific networks and establish the uniqueness of the Nash equilibrium in these networks, as well as the uniqueness of link utilization at Nash equilibria for specific cost functions in networks with general topology. We also present a result for convergence to equilibria from an initial nonequilibrium state.

This paper studies two problems that arise in distributed computing. We deal with these problems from a game theoretical approach. We are interested in the convergence to the Nash equilibrium of algorithms based on the best reply strategy in a special case of linear costs. We present three specific types of algorithm that converge to the equilibrium. In our first model, composed of two processors, the convergence is established through monotonicity of the sequence of updates generated by each of the three algorithms. In the second model, made up of N processors, the convergence is due to the contraction of the algorithms.