On the existence of equilibria in noncooperative optimal flow control
Journal of the ACM (JACM)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Algorithms, games, and the internet
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Topological Conditions for Uniqueness of Equilibrium in Networks
Mathematics of Operations Research
Topological Uniqueness of the Nash Equilibrium for Selfish Routing with Atomic Users
Mathematics of Operations Research
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Architecting noncooperative networks
IEEE Journal on Selected Areas in Communications
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We study the problem of routing traffic through a congested network consisting of m parallel links, each having a certain speed. Moreover, we are given n selfish (non-cooperative) agents, each of them willing to route her own piece of traffic on exactly one link. Agents are selfish in that they only pick a link which minimize the delay of their own piece of traffic. In this context 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 thus enter a steady state from which no agent is willing to unilaterally deviate. In this work we consider situations in which some agents have constraints on the routing choice: in a sense they are forbidden to route their traffic on some links. We show that at most one Nash equilibrium may exist and, in some cases with equal speed links and where each agent is forbidden to route on at most one link, we give necessary and sufficient conditions on its existence; these conditions correlate the traffic load of the agents. We consider also a dynamic behaviour of the network when the constraints may vary, in particular when a constraint is removed: we establish under which conditions the network is still in equilibrium. These conditions are all effective in the sense that, given a set of yes/no routing constraints on each link for each agent, we provide the probability distributions corresponding to the unique Nash equilibrium associated to the constraints (if it exists). Moreover these conditions and the possible Nash equilibrium are computed in time O(mn).