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Journal Articles Networks Year : 2016

Finding a Nash Equilibrium and an optimal sharing policy for multi-agent network expansion game

Abstract

In this work, a multi-agent network flow problem is addressed , aiming at characterizing the properties of stable flows and allowing their computation. Two types of agents are considered: transportation-agents, that carry a flow of products on a given network and another agent, either a producer or a customer, who is willing to ship (receive, respectively) products. Every transportation-agent controls a set of arcs, each having a capacity that can be increased up to a certain point at a given cost. The other agent (i.e., the customer/producer) is interested in maximizing the flow transshipped through the network. To this aim, we assume it offers the transportation-agents a reward that is proportional to the realized flow value. This particular multi-agent framework is referred to as a Multi-Agent network expansion game. We characterize and find particular stable strategies (i.e., Nash equilibria) that are of interest for this game. We particularly focus on the problem of finding a Nash Equilibrium and a sharing policy that maximize the value of the total flow. We prove that this problem is NP-hard in the strong sense and show how such a strategy can be characterized considering paths in specific auxiliary graphs. We also provide a mixed integer linear programming (MILP) formulation to solve the problem. Computational experiments are provided to prove the effectiveness of our approach and derive some insights for practitioners.
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Dates and versions

hal-01383580 , version 1 (18-10-2016)

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Nadia Chaabane, Alessandro Agnetis, Cyril Briand, Marie-José Huguet. Finding a Nash Equilibrium and an optimal sharing policy for multi-agent network expansion game. Networks, 2016, 69 (1), pp.94-109. ⟨10.1002/net.21711⟩. ⟨hal-01383580⟩
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