Cooperative Network Design: a Nash bargaining solution approach Konstantin Avrachenkov a , Jocelyne Elias b , Fabio Martignon 1,c,∗ , Giovanni Neglia a , Leon Petrosyan d a INRIA Sophia Antipolis, France. b Paris Descartes University, France. c IUF, Institut Universitaire de France d St. Petersburg State University, Russia. Abstract The Network Design problem has received increasing attention in recent years. Previ- ous works have addressed this problem considering almost exclusively networks designed by selfish users, which can be consistently suboptimal. This paper addresses the network design issue using cooperative game theory, which permits to study ways to enforce and sustain cooperation among users. Both the Nash bargaining solution and the Shapley value are widely applicable concepts for solving these games. However, the Shapley value presents several drawbacks in this context. For this reason, we solve the cooperative network design game using the Nash bar- gaining solution (NBS) concept. More specifically, we extend the NBS approach to the case of multiple players and give an explicit expression for users’ cost allocations. We fur- ther provide a distributed algorithm for computing the Nash bargaining solution. Then, we compare the NBS to the Shapley value and the Nash equilibrium solution in several network scenarios, including real ISP topologies, showing its advantages and appeal- ing properties in terms of cost allocation to users and computation time to obtain the solution. Numerical results demonstrate that the proposed Nash bargaining solution approach permits to allocate costs fairly to users in a reasonable computation time, thus repre- senting a very effective framework for the design of efficient and stable networks. Index Terms : - Network Design, Cooperative Game Theory, Nash bargaining solution, Shapley value. * Corresponding author, Tel: (+33) 01.69.15.68.16, Fax: (+33) 01.69.15.65.86 Email addresses: K.Avrachenkov@sophia.inria.fr (Konstantin Avrachenkov), jocelyne.elias@parisdescartes.fr (Jocelyne Elias), fabio.martignon@lri.fr (Fabio Martignon), Giovanni.Neglia@sophia.inria.fr (Giovanni Neglia), spbuoasis7@peterlink.ru (Leon Petrosyan) Preprint submitted to Elsevier Computer Networks March 27, 2015