Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Chen, B., Cheng, H.H.: A review of the applications of agent technology in traffic and transportation systems. IEEE Trans. Intell. Transp. Syst. 11(2), 485–497 (2010)
Pechoucek, M., Marik, V.: Industrial deployment of multi-agent technologies: review and selected case studies. Auton. Agent. Multi-Agent Syst. 17(3), 397–431 (2008)
Briand, C., Agnetis, A., Billaut, J.C.: The multiagent project scheduling problem: complexity of finding an optimal Nash equilibrium. In: Proceedings of PMS Conference, pp. 106–109 (2012)
Zhang, F., Roundy, R., Akanyildrim, M.C., Huh, W.T.: Optimal capacity expansion for multi-product, multi-machine manufacturing systems with stochastic demand. IIE Trans. 36(1), 23–26 (2004)
Malcolm, S., Zenios, S.: Robust optimization for power systems capacity expansion under uncertainty. J. Oper. Res. Soc. 45(9), 1040–1049 (1994)
Laguna, M.: Applying robust optimization to capacity expansion of one location in telecommunications with demand uncertainty. Manage. Sci. 44(11), 101–110 (1998)
Hsu, V.N.: Dynamic capacity expansion problem with deferred expansion and age-dependent shortage cost. Manage. Sci. 4(1), 44–54 (2002)
Magnanti, T., Wong, R.: Network design and transportation planning: models and algorithms. Transp. Sci. 18(1), 1–55 (1984)
Fulkerson, D.R.: Increasing the capacity of a network: the parametric budget problem. Manage. Sci. 5(4), 472–483 (1959)
Ordonez, F., Zhao, J.: Robust capacity expansion of network flow. Networks 50(2), 136–145 (2007)
Tardos, E., Wexler, T.: Network formation games and the potential function method. In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V. (eds.) Algorithmic Game Theory, pp. 487–516. Cambridge University Press, Cambridge (2007)
Apt, K.R., Markakis, E.: Diffusion in social networks with competing products. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 212–223. Springer, Heidelberg (2011)
Resnick, E., Bachrach, Y., Meir, R., Rosenschein, J.S.: The cost of stability in network flow games. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 636–650. Springer, Heidelberg (2009)
Evaristo, R., Van Fenema, P.C.: A typology of project management: emergence and evolution of new forms. Int. J. Proj. Manage. 17(5), 275–281 (1999)
De, P., Dunne, E.J., Ghosh, J.B., Wells, C.E.: Complexity of the discrete time-cost tradeoff problem for project networks. Eur. J. Oper. Res. 45(2), 302–306 (1997)
Estevez, M.A.: Fernandez: a game theoretical approach to sharing penalties and rewards in projects. Eur. J. Oper. Res. 216(3), 647–657 (2012)
Agnetis, A., Briand, C., Billaut, J.-C., Sucha, P.: Nash equilibria for the multi-agent project scheduling problem with controllable processing times. J. Sched. 18(1), 15–27 (2014)
Kamburowski, J.: On the minimum cost project schedule. Int. J. Manage. Sci. 22(4), 401–407 (1994)
Briand, C., Sucha, P., Ngueveu, S.U.: Finding an optimal Nash equilibrium to the multi-agent project scheduling problem. J. Oper. Res (Submitted to)
Cachon, G.P., Lariviere, M.A.: Supply chain coordination with revenue-sharing contracts: strengths and limitations. Int. J. Manage. Sci. 51(1), 30–44 (2005)
Ehrgott, M.: Multicriteria Optimization. Algorithmic Game Theory, pp. 487–516. Springer, New York (2005)
Ford, L.R., Fulkerson, D.R.: Flow in Networks. Princeton University Press, Princeton (1958)
Nash, J.: Equilibrium points in n-person games. Proc. Natl. Acad. Sci. 36(1), 48–49 (1950)
Nash, J.: Non-cooperative games. Ann. Math. 54(2), 286–295 (1951)
Shoham, Y., Leyton-Brown, K.: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, New York (2009). ISBN 978-0-521-89943-7
Busacker, R.G., Gowen, P.J.: A Procedure for Determining a Family of Minimal-Cost Network Flow Patterns. Defense Technical Information Center, 15th edn. (1961)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman & Co., New York (1979)
Acknowledgements
This work was supported by the ANR project no. ANR-13-BS02-0006-01 named Athena.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Fakhfakh, N.C., Briand, C., Huguet, MJ. (2015). Nash Equilibria for Multi-agent Network Flow with Controllable Capacities. In: Pinson, E., Valente, F., Vitoriano, B. (eds) Operations Research and Enterprise Systems. ICORES 2014. Communications in Computer and Information Science, vol 509. Springer, Cham. https://doi.org/10.1007/978-3-319-17509-6_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-17509-6_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17508-9
Online ISBN: 978-3-319-17509-6
eBook Packages: Computer ScienceComputer Science (R0)