Topological Uniqueness of the Nash Equilibrium for Selfish Routing with Atomic Users

References

• Altman E., Kameda H. Equilibria for multiclass routing in multi-agent networks. Proc. 40th IEEE Conf. Decision and Control (2001) Orlando, FL:604–609Google Scholar
• Altman E., Başar T., Jiménez T., Shimkin N. Competitive routing in networks with polynomial cost. IEEE Trans. Automatic Control (2002) 47:92–96Crossref, Google Scholar
• Altman E., Boulogne T., El Azouzi R., Jiménez T., Wynter L. A survey on networking games in telecommunications. Comput. Oper. Res. (2005) 33(2):286–311Crossref, Google Scholar
• Azouzi R., Altman E. Constrained traffic equilibrium in routing. IEEE Trans. Automatic Control (2003) 48(9):1656–1660Crossref, Google Scholar
• Beckmann M., McGuire C. B., Winsten C. B.Studies in the Economics of Transportation (1956) (Yale University Press, New Haven, CT) Google Scholar
• Boulogne T., Altman E., Kameda H., Pourtallier O. Mixed equilibrium (ME) for multiclass routing games. IEEE Trans. Automatic Control (2002) 47(6):903–916Crossref, Google Scholar
• Dafermos S. C. An extended traffic assignment model with application to two-way traffic transportation science. Transportation Sci. (1971) 5:366–389Link, Google Scholar
• Dafermos S. C. The traffic assignment problem for multiclass-user transportation networks. Transportation Sci. (1972) 6:73–87Link, Google Scholar
• Dafermos S. C., Sparrow F. T. The traffic assignment problem for a general network. J. Res. National Bureau Standards (1969) 37B:91–118Google Scholar
• Debreu G. A social equilibrium existence theorem. Proc. National Acad. Sci. (1952) 38:886–893Google Scholar
• Devarajan S. A note on network equilibrium and noncooperative games. Transportation Res. Part B (1981) 15B:421–426Crossref, Google Scholar
• El Azouzi R., Altman E., Pourtallier O. Avoiding paradoxes in multi-agent competitive routing. Comput. Networks (2003) 43:133–146Crossref, Google Scholar
• Harker P. Multiple equilibrium behaviors on networks. Transportation Sci. (1988) 22:39–46Link, Google Scholar
• Haurie A., Marcotte P. On the relationship between Nash-Cournot and Wardrop equilibria. Networks (1985) 15:295–308Crossref, Google Scholar
• Jiménez T., Altman E., Başar T., Shimkin N. Routing into two parallel links: Game-theoretic distributed algorithms. J. Parallel Distributed Comput. (2001) 61:1367–1381(Special Issue on Routing in Computer and Communication Systems)Crossref, Google Scholar
• Khan M. A. On extensions to the Cournot-Nash theorem. Advances in Equilibrium Theory. Lecture Notes Economic Mathematical Systems (1985) 244(Springer-Verlag)79–106Google Scholar
• Korilis Y., Lazar A., Orda A. Architecting noncooperative networks. IEEE J. Selected Areas Comm. (1995) 13(7):1241–1251Crossref, Google Scholar
• Korilis Y., Lazar A., Orda A. Capacity allocation under noncooperative routing. IEEE Trans. Automatic Control (1997) 42(3):309–325Crossref, Google Scholar
• Korilis Y., Lazar A., Orda A. Avoiding the Braess paradox in non-cooperative networks. J. Appl. Probab. (1999) 36:211–222Crossref, Google Scholar
• Korilis Y. A., Varvarigou T. A., Ahuja S. R. Incentive-compatible pricing strategies in noncooperative networks. Proc. IEEE INFOCOM’98, San Francisco, CA (1998) 439–446Google Scholar
• La R. J., Anantharam V. Optimal routing control: Repeated game approach. IEEE Trans. Automatic Control (2002) 47:437–450Crossref, Google Scholar
• Marcotte P., Wynter L. A new look at the multiclass network equilibrium problem. Transportation Sci. (2004) 38(3):282–292Link, Google Scholar
• Milchtaich I. Topological conditions for uniqueness of equilibrium in networks. Math. Oper. Res. (2005) 30:225–244Link, Google Scholar
• Nagurney A.Network Economics: A Variational Inequality Approach (1999) 2nd ed.(Kluwer Academic, Dordrecht, The Netherlands) Crossref, Google Scholar
• Orda A., Rom R., Shimkin N. Competitive routing in multi-user communication networks. IEEE/ACM Trans. Networking (1993) 1(5):510–521Crossref, Google Scholar
• Patriksson M.The Traffic Assignment Problem: Models and Methods (1994) (VSP, Utrecht, The Netherlands) Google Scholar
• Rath K. P. A direct proof of the existence of pure strategy equilibria in games with a continuum of players. Econom. Theory (1992) 2:427–433Crossref, Google Scholar
• Rosen J. B. Existence and uniqueness of equilibrium points for concave n-person games. Econometrica (1965) 33(3):520–534Crossref, Google Scholar
• Roughgarden T.Selfish Routing and the Price of Anarchy (2005) (MIT Press, Cambridge, MA) Google Scholar
• Roughgarden T., Tardos E. How bad is selfish routing? J. ACM (2002) 49:236–259Crossref, Google Scholar
• Schmeidler D. Equilibrium points of nonatomic games. J. Statist. Phys. (1973) 7(4):295–300Crossref, Google Scholar
• Wardrop J. G. Some theoretical aspects of road traffic research. Proc. Inst. Civil Engrg. (1952) 2:325–378Google Scholar