Matroids Are Immune to Braess’ Paradox

Published Online:https://doi.org/10.1287/moor.2016.0825

References

  • Ackermann H, Röglin H, Vöcking B (2008) On the impact of combinatorial structure on congestion games. J. ACM 55(6):1–22.CrossrefGoogle Scholar
  • Ackermann H, Röglin H, Vöcking B (2009) Pure Nash equilibria in player-specific and weighted congestion games. Theoret. Comput. Sci. 410(17):1552–1563.CrossrefGoogle Scholar
  • Balinski ML (1961) On the graph structure of convex polyhedra in n-space. Pacific J. Math. 11(2):431–434.CrossrefGoogle Scholar
  • Beckmann M, McGuire C, Winsten C (1956) Studies in the Economics of Transportation (Yale University Press, New Haven, CT).Google Scholar
  • Bhaskar U, Fleischer L, Hoy D, Huang C (2015) On the uniqueness of equilibrium in atomic splittable routing games. Math. Oper. Res. 40(3):634–654.LinkGoogle Scholar
  • Braess D (1968) Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung 12(1):258–268.Google Scholar
  • Braess D, Nagurney A, Wakolbinger T (2005) On a paradox of traffic planning. Transportation Sci. 39(4):446–450.LinkGoogle Scholar
  • Catoni S, Pallotino S (1991) Traffic equilibrium paradoxes. Transportation Sci. 25(3):240–244.LinkGoogle Scholar
  • Cenciarelli P, Gorla D, Salvo I (2016) Graph theoretic investigations on inefficiencies in network models. Preprint arXiv:1603.01983.Google Scholar
  • Chen X, Diao Z, Hu X (2015) Excluding Braess’s paradox in nonatomic selfish routing. Hoefer M, ed. Proc. 8th Internat. Sympos. Algorithmic Game Theory, Lecture Notes in Computer Science, Vol. 9347 (Springer, Berlin), 219–230.CrossrefGoogle Scholar
  • Cohen J, Kelly F (1990) A paradox of congestion in a queuing network. J. Appl. Prob. 27(3):730–734.CrossrefGoogle Scholar
  • Cohen JE, Horowitz P (1991) Paradoxial behaviour of mechanical and electrical networks. Nature 352(6337):699–701.CrossrefGoogle Scholar
  • Cominetti R, Correa JR, Stier-Moses NE (2009) The impact of oligopolistic competition in networks. Oper. Res. 57(6):1421–1437.LinkGoogle Scholar
  • Correa JR, Stier-Moses NE (2011) Wardrop equilibria. Cochran JJ, Cox LA Jr, Keskinocak P, Kharoufeh JP, Smith JC, eds. Wiley Encyclopedia of Operations Research and Management Science (John Wiley & Sons, New York).CrossrefGoogle Scholar
  • Correa JR, Schulz AS, Stier-Moses NE (2004) Selfish routing in capacitated networks. Math. Oper. Res. 29(4):961–976.LinkGoogle Scholar
  • Dafermos S, Nagurney A (1984) On some traffic equilibrium theory paradoxes. Transportation Res. Part B: Methodological 18(2): 101–110.CrossrefGoogle Scholar
  • Edmonds J (1971) Submodular functions, matroids, and certain polyhedra. Guy R, ed. Combinatorial Structures and Their Applications (Gordon and Breach, New York), 69–87.Google Scholar
  • Epstein A, Feldman M, Mansour Y (2009) Efficient graph topologies in network routing games. Games Econom. Behav. 66(1):115–125.CrossrefGoogle Scholar
  • Fotakis D, Kaporis AC, Lianeas T, Spirakis PG (2013) Resolving Braess’s paradox in random networks. Chen Y, Immorlica N, eds. Proc. 9th Internat. Conf. Web Internet Econom. (Springer, Berlin), 188–201.CrossrefGoogle Scholar
  • Frank M (1981) The Braess paradox. Math. Programming 20(1):283–302.CrossrefGoogle Scholar
  • Fujishige S (2005) Submodular Functions and Optimization (Elsevier, Amsterdam).Google Scholar
  • Hagstrom JN, Abrams RA (2001) Characterizing Braess’s paradox for traffic networks. Proc. IEEE 2001 Conf. Intelligent Transportation Systems (IEEE, Piscataway, NJ), 836–841.CrossrefGoogle Scholar
  • Harks T (2011) Stackelberg strategies and collusion in network games with splittable flow. Theory Comput. Systems 48(4):781–802.CrossrefGoogle Scholar
  • Harks T, Peis B (2014) Resource buying games. Algorithmica 70(3):493–512.CrossrefGoogle Scholar
  • Harks T, Klimm M, Peis B (2014) Resource competition on integral polymatroids. Liu T-Y, Qi Q, Ye Y, eds. Web and Internet Economics. Lecture Notes in Computer Science, Vol. 8877 (Springer, Berlin), 189–202.CrossrefGoogle Scholar
  • Holzman R, Law-Yone N (1997) Strong equilibrium in congestion games. Games Econom. Behav. 21(1–2):85–101.CrossrefGoogle Scholar
  • Holzman R, Law-Yone N (2003) Network structure and strong equilibrium in route selection games. Math. Soc. Sci. 46(2):193–205.CrossrefGoogle Scholar
  • Kameda H (2002) How harmful the paradox can be in the Braess/Cohen-Kelly-Jeffries networks. IEEE INFOCOM (IEEE, Piscataway, NJ), 437–445.CrossrefGoogle Scholar
  • Kameda H, Altman E, Kozawa T, Hosokawa Y (2000) Braess-like paradoxes in distributed computer systems. IEEE Trans. Automatic Control 45(9):1687–1691.CrossrefGoogle Scholar
  • Korilis YA, Lazar AA, Orda A (1999) Avoiding the Braess paradox in noncooperative networks. J. Appl. Probab. 36(1):211–222.CrossrefGoogle Scholar
  • Lin HC, Roughgarden T, Tardos É, Walkover A (2011) Stronger bounds on Braess’s paradox and the maximum latency of selfish routing. SIAM J. Discrete Math. 25(4):1667–1686.CrossrefGoogle Scholar
  • Milchtaich I (1996) Congestion models of competition. Amer. Naturalist 147(5):760–783.CrossrefGoogle Scholar
  • Milchtaich I (2005) Topological conditions for uniqueness of equilibrium in networks. Math. Oper. Res. 30(1):225–244.LinkGoogle Scholar
  • Milchtaich I (2006) Network topology and the efficiency of equilibrium. Games Econom. Behav. 57(2):321–346.CrossrefGoogle Scholar
  • Murota K (2003) Discrete Convex Analysis (SIAM, Philadelphia).CrossrefGoogle Scholar
  • Oxley JG (1992) Matroid Theory (Oxford University Press, Oxford, UK).Google Scholar
  • Pas EI, Principio SL (1997) Braess’ paradox: Some new insights. Transportation Res. Part B: Methodological 31(3):265–276.CrossrefGoogle Scholar
  • Pöppe C (1992) Paradoxes Verhalten physikalischer und ökonomischer Systeme. Spektrum der Wissenschaft (November):23–26.Google Scholar
  • Qiu L, Yang Y, Zhang Y, Shenker S (2006) On selfish routing in Internet-like environments. IEEE/ACM Trans. Networking 14(4): 725–738.CrossrefGoogle Scholar
  • Richman O, Shimkin N (2007) Topological uniqueness of the Nash equilibrium for selfish routing with atomic users. Math. Oper. Res. 32(1):215–232.LinkGoogle Scholar
  • Rosenthal R (1973) A class of games possessing pure-strategy Nash equilibria. Internat. J. Game Theory 2(1):65–67.CrossrefGoogle Scholar
  • Rosenthal R (1973) The network equilibrium problem in integers. Networks 3(1):53–59.CrossrefGoogle Scholar
  • Roughgarden T (2002) Selfish routing. Unpublished doctoral dissertation, Cornell University, Ithaca, NY.Google Scholar
  • Roughgarden T (2002) The price of anarchy is independent of the network topology. J. Comput. System Sci. 67(2):341–364.CrossrefGoogle Scholar
  • Roughgarden T (2006) On the severity of Braess’s paradox: Designing networks for selfish users is hard. J. Comput. System Sci. 72(5):922–953.CrossrefGoogle Scholar
  • Roughgarden T, Schoppmann F (2015) Local smoothness and the price of anarchy in splittable congestion games. J. Econom. Theory 156(March):317–342.CrossrefGoogle Scholar
  • Roughgarden T, Tardos É (2002) How bad is selfish routing? J. ACM 49(2):236–259.CrossrefGoogle Scholar
  • Samuelson P (1992) Tragedy of the open road: Avoiding paradox by use of regulated public utilities that charge corrected Knightian tolls. J. Internat. Comparative Econom.: JOICE 1(1):3–12.Google Scholar
  • Schrijver A (2003) Combinatorial Optimization: Polyhedra and Efficiency (Springer, Berlin).Google Scholar
  • Smith M (1978) In a road network, increasing delay locally can reduce delay globally. Transportation Res. 12(6):419–422.CrossrefGoogle Scholar
  • Steinberg R, Zangwill W (1983) The prevalence of Braess’s paradox. Transportation Sci. 17(3):301–318.LinkGoogle Scholar
  • Thomas RR (1998) Applications to integer programming. Cox DA, Sturmfels B, eds. Proc. Symposia Appl. Math., Vol. 53 (American Mathematical Society, Providence, RI), 119–141.Google Scholar
  • Valiant G, Roughgarden T (2010) Braess’s paradox in large random graphs. Random Structures Algorithms 37(4):495–515.CrossrefGoogle Scholar
  • Wardrop J (1952) Some theoretical aspects of road traffic research. Proc. Inst. Civil Engrg. 1(Part II):325–378.CrossrefGoogle Scholar
  • Welsh DJA (2010) Matroid Theory. First published by Academic Press, 1976 (Dover, New York).Google Scholar
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