Nash Equilibria for multi-agent network flow with controllable capacities

Nadia Chaabane (1, 2) , Cyril Briand (2, 3) , Marie-José Huguet (2, 1)

1 INSA Toulouse - Institut National des Sciences Appliquées - Toulouse
2 LAAS-ROC - Équipe Recherche Opérationnelle, Optimisation Combinatoire et Contraintes
3 UT3 - Université Toulouse III - Paul Sabatier

In this work, a multi-agent network flow problem is addressed where a set of transportation-agents can control the capacities of a set of elementary routes A third-party agent, a customer, is interesting in maximizing the product flow transshipped from a source to a sink node through the network and offers a reward that is proportional to the flow value the transportation agents manage to provide. This problem can be viewed as a Multi-Agent Minimum-Cost Maximum-Flow Problem where the focus is put on finding stable strategies (i.e., Nash Equilibria) such that no transportation-agent has any incentive to modify its behavior. We show how such an equilibrium can be characterized by means of augmenting or decreasing paths in a reduced network. We also discuss the problem of finding a Nash Equilibrium that maximizes the flow and prove its NP-Hardness.

Mots clés: Multi-Agent Network flow; Nash Equilibria; Complexity; Min-Cost Max-Flow

Domaines: Recherche opérationnelle [math.OC]

Nadia Chaabane, Cyril Briand, Marie-José Huguet. Nash Equilibria for multi-agent network flow with controllable capacities. Communications in Computer and Information Science, 2015, Operations Research and Enterprise Systems, 509, pp.47-62. ⟨10.1007/978-3-319-17509-6_4⟩. ⟨hal-01166010⟩