A Sensitivity Analysis of the Price of Anarchy in Nonatomic Congestion Games

Published Online:https://doi.org/10.1287/moor.2022.1292

References

  • [1] Beckmann MJ, McGuire C, Winsten CB (1956) Studies in the Economics of Transportation (Yale University Press, New Haven, CT).Google Scholar
  • [2] Bingham NH, Goldie CM, Teugels JL (1987) Regular Variation (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [3] Bureau of Public Roads (1964) Traffic Assignment Manual (U.S. Department of Commerce, Urban Planning Division, Washington, DC).Google Scholar
  • [4] Colini-Baldeschi R, Cominetti R, Scarsini M (2016) On the price of anarchy of highly congested nonatomic network games. Gairing M, Savani R, eds. Algorithmic Game Theory, Lecture Notes in Computer Science, vol. 9928 (Springer, Berlin, Heidelberg), 117–128.CrossrefGoogle Scholar
  • [5] Colini-Baldeschi R, Cominetti R, Mertikopoulos P, Scarsini M (2017) The asymptotic behavior of the price of anarchy. Devanur NR, Lu P, eds. Web and Internet Economics, Lecture Notes in Computer Science, vol. 10660 (Springer, Cham, Switzerland), 133–145 .CrossrefGoogle Scholar
  • [6] Colini-Baldeschi R, Cominetti R, Mertikopoulos P, Scarsini M (2020) When is selfish routing bad? The price of anarchy in light and heavy traffic. Oper. Res. 68(2):411–434.AbstractGoogle Scholar
  • [7] Cominetti R, Dose V, Scarsini M (2021) The price of anarchy in routing games as a function of the demand. Math. Programming, ePub ahead of print September 8, https://doi.org/10.1007/s10107-021-01701-7.Google Scholar
  • [8] Correa JR, Schulz AS, Stier Moses NE (2004) Selfish routing in capacitated networks. Math. Oper. Res. 29(4):961–976.LinkGoogle Scholar
  • [9] Correa JR, Schulz AS, Stier-Moses NE (2005) On the inefficiency of equilibria in congestion games. Jünger M, Kaibel V, eds. Integer Programming and Combinatorial Optimization, Internat. IPCO Conf., Lecture Notes in Computer Science, vol. 3509 (Springer, Berlin, Heidelberg), 167–181.Google Scholar
  • [10] Dafermos S (1980) Traffic equilibrium and variational inequalities. Transportation Sci. 14(1):42–54.LinkGoogle Scholar
  • [11] Dafermos SC, Sparrow FT (1969) The traffic assignment problem for a general network. J. Res. U.S. National Bureau Standards 73(B):91–118.Google Scholar
  • [12] Englert M, Franke T, Olbrich L (2010) Sensitivity of Wardrop equilibria. Theory Comput. Systems 47(1):3–14.CrossrefGoogle Scholar
  • [13] Hall M (1978) Properties of the equilibrium state in transportation networks. Transportation. Sci. 12(3):208–216.LinkGoogle Scholar
  • [14] Harks T, Kleinert I, Klimm M, Möhring RH (2015) Computing network tolls with support constraints. Networks 65(3):262–285.CrossrefGoogle Scholar
  • [15] Jahn O, Möhring RH, Schulz AS, Stier-Moses NE (2005) System-optimal routing of traffic flows with user constraints in networks with congestion. Oper. Res. 53(4):600–616.LinkGoogle Scholar
  • [16] Josefsson M, Patriksson M (2007) Sensitivity analysis of separable traffic equilibrium equilibria with application to bilevel optimization in network design. Transportation Res. Part B: Methodological 41(1):4–31.CrossrefGoogle Scholar
  • [17] Kelley J (1975) General Topology (Springer, Berlin).Google Scholar
  • [18] Klimm M, Warode P (2019) Computing all Wardrop equilibria parametrized by the flow demand. Proc. 30th Annual ACM-SIAM Sympos. Discrete Algorithms (SIAM, Philadelphia), 917–934.Google Scholar
  • [19] Klimm M, Warode P (2022) Parametric computation of minimum-cost flows with piece-wise quadratic costs. Math. Oper. Res. 47(1):812–846.LinkGoogle Scholar
  • [20] Koutsoupias E, Papadimitriou CH (1999) Worst-case equilibria. Proc. 16th Annual Sympos. Theoret. Aspects Comput. Sci. (STACS), Lecture Notes in Computer Science, vol. 1563 (Springer, Heidelberg), 404–413.Google Scholar
  • [21] Lu S (2008) Sensitivity of static traffic user equilibria with perturbations in arc cost function and travel demand. Transportation Sci. 42(1):105–123.LinkGoogle Scholar
  • [22] Monnot B, Benita F, Piliouras G (2017) How bad is selfish routing in practice? Preprint, submitted March 5, https://arxiv.org/abs/1703.01599.Google Scholar
  • [23] Nisan N, Roughgarden T, Tardos E, Vaz VV (2007) Algorithmic Game Theory (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • [24] O’Hare SJ, Connors RD, Watling DP (2016) Mechanisms that govern how the price of anarchy varies with travel demand. Transportation Res. Part B: Methodological 84:55–80.CrossrefGoogle Scholar
  • [25] Papadimitriou C (2001) Algorithms, games, and the internet. Proc. Thirty-third Annual ACM Sympos. Theory Comput. (ACM, New York), 749–753.Google Scholar
  • [26] Patriksson M (2004) Sensitivity analysis of traffic equilibria. Transportation Sci. 38(3):258–281.LinkGoogle Scholar
  • [27] Perakis G (2007) The price of anarchy under nonlinear and asymmetric costs. Math. Oper. Res. 32(3):614–628.LinkGoogle Scholar
  • [28] Pigou AC (1920) The Economics of Welfare, 1st ed. (Macmillan and Co., London).Google Scholar
  • [29] Rosenthal RW (1973) A class of games possessing pure-strategy Nash equilibria. Internat. J. Game Theory 2(1):65–67.CrossrefGoogle Scholar
  • [30] Roughgarden T (2001) Designing networks for selfish users is hard. Proc. 42nd Annual Sympos. Foundations Comput. Sci. (IEEE Computer Society, Washington, DC), 472–481.Google Scholar
  • [31] Roughgarden T (2003) The price of anarchy is independent of the network topology. J. Comput. System Sci. 67(2):341–364.CrossrefGoogle Scholar
  • [32] Roughgarden T (2005) Selfish Routing and the Price of Anarchy (The MIT Press, Cambridge, MA).Google Scholar
  • [33] Roughgarden T (2015) Intrinsic robustness of the price of anarchy. J. ACM 62(5):1–42.CrossrefGoogle Scholar
  • [34] Roughgarden T, Tardos E (2002) How bad is selfish routing? J. ACM 49(2):236–259.CrossrefGoogle Scholar
  • [35] Roughgarden T, Tardos E (2004) Bounding the inefficiency of equilibria in nonatomic congestion games. Games Econom. Behav. 47(2):389–403.CrossrefGoogle Scholar
  • [36] Roughgarden T, Tardos E (2007) Introduction to the inefficiency of equilibria. Nisan N, Roughgarden T, Tardos É, Vazirani VV, eds. Algorithmic Game Theory (Cambridge University Press, Cambridge, UK), 443–459.CrossrefGoogle Scholar
  • [37] Sandholm WH (2001) Potential games with continuous player sets. J. Econom. Theory 97(1):81–108.CrossrefGoogle Scholar
  • [38] Schmeidler D (1973) Equilibrium points of nonatomic games. J. Statist. Phys. 7(4):295–300.CrossrefGoogle Scholar
  • [39] Smith MJ (1979) The existence, uniqueness and stability of traffic equilibria. Transportation Res. Part B: Methodological 13(4):295–304.CrossrefGoogle Scholar
  • [40] Takalloo M, Kwon C (2020) Sensitivity of Wardrop equilibria: Revisited. Optim. Lett. 14(3):781–796.CrossrefGoogle Scholar
  • [41] Wardrop JG (1952) Some theoretical aspects of road traffic research. Proc. Inst. Civil Engineers 1(3):325–362.Google Scholar
  • [42] Wu Z, Möhring R, Chen Y, Xu D (2021) Selfishness need not be bad. Oper. Res. 69(2):410–435.LinkGoogle Scholar
  • [43] Youn H, Gastner MT, Jeong H (2008) Price of anarchy in transportation networks: Efficiency and optimality control. Phys. Rev. Lett. 101(12):128701.CrossrefGoogle Scholar
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