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Network Topologies for Weakly Pareto Optimal Nonatomic Selfish Routing

  • Xujin Chen
  • Zhuo DiaoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)

Abstract

In this paper we study the model of nonatomic selfish routing and characterize the topologies of undirected/directed networks in which every Nash equilibrium is weakly Pareto optimal, meaning that no deviation of all players could make everybody better off. In particular, we first obtain the characterizations for single-commodity case by applying relatively standard graphical arguments, and then the counterpart for two-commodity undirected case by introducing some new algorithmic ideas and reduction techniques.

Keywords

Nonatomic selfish routing Weakly Pareto optimal Single-commodity networks Multi-commodity networks Extension-parallel networks 

References

  1. 1.
    Beckmann, M.J., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)Google Scholar
  2. 2.
    Braess, D.: Über ein paradoxon aus der verkehrsplanung. Unternehmensforschung 12(1), 258–268 (1968)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Chen, X., Chen, Z., Hu, X.: Excluding braess’s paradox in nonatomic selfish routing. In: Hoefer, M., et al. (eds.) SAGT 2015. LNCS, vol. 9347, pp. 219–230. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-48433-3_17 Google Scholar
  4. 4.
    Epstein, A., Feldman, M., Mansour, Y.: Efficient graph topologies in network routing games. Games Econ. Behav. 66(1), 115–125 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Holzman, R., yone (Lev-tov), N.L.: Strong equilibrium in congestion games. Games Econ. Behav 21(1–2), 85–101 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Holzman, R., yone (Lev-tov), N.L.: Network structure and strong equilibrium in route selection games. Math. Soc. Sci. 46(2), 193–205 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Holzman, R., Monderer, D.: Strong equilibrium in network congestion games: increasing versus decreasing costs. Int. J. Game Theory 44, 647–666 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Milchtaich, I.: Network topology and the efficiency of equilibrium. Games and Econ. Behav. 57(2), 321–346 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series parallel digraphs. SIAM J. Comput. 11(2), 298 (1982)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Applied MathematicsAMSS, Chinese Academy of SciencesBeijingChina

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