Equilibria in Multiclass and Multidimensional Atomic Congestion Games

References

• [1] Aashtiani HZ, Magnanti TL (1981) Equilibria on a congested transportation network. SIAM J. Algebraic Discrete Methods 2(3):213–226.Crossref, Google Scholar
• [2] Abdulaal M, LeBlanc LJ (1979) Methods for combining modal split and equilibrium assignment models. Transportation Sci. 13(4):292–314.Link, Google Scholar
• [3] Ackermann H, Röglin H, Vöcking B (2008) On the impact of combinatorial structure on congestion games. J. ACM 55(6):1–22.Crossref, Google Scholar
• [4] Ackermann H, Röglin H, Vöcking B (2009) Pure Nash equilibria in player-specific and weighted congestion games. Theoret. Comput. Sci. 410(17):1552–1563.Crossref, Google Scholar
• [5] Alvarez Lopez P, Behrisch M, Bieker-Walz L, Erdmann J, Flötteröd YP, Hilbrich R, Lücken L, Rummel J, Wagner P, Wießner E (2018) Microscopic traffic simulation using SUMO. Proc. 21st IEEE Internat. Conf. Intelligent Transportation Systems (Institute of Electrical and Electronics Engineers, Piscataway, NJ).Google Scholar
• [6] Andelman N, Feldman M, Mansour Y (2009) Strong price of anarchy. Games Econom. Behav. 65(2):289–317.Crossref, Google Scholar
• [7] Anshelevich E, Dasgupta A, Kleinberg J, Tardos É, Wexler T, Roughgarden T (2008) The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4):1602–1623.Crossref, Google Scholar
• [8] Aumann R (1959) Acceptable points in general cooperative n-person games. Luce R, Tucker A, eds. Contributions to the Theory of Games, Vol. IV (Princeton University Press, Princeton, NJ), 287–324.Crossref, Google Scholar
• [9] Beckmann M, McGuire CB, Winsten CB (1956) Studies in the Economics and Transportation (Yale University Press, New Haven, CT).Google Scholar
• [10] Branston D, van Zylen H (1978) The estimation of saturation flow, effective green time and passenger car equivalents at traffic signals by multiple linear regression. Transportation Res. 12(1):47–53.Crossref, Google Scholar
• [11] Caragiannis I, Fanelli A, Gravin N, Skopalik A (2012) Approximate pure Nash equilibria in weighted congestion games: Existence, efficient computation, and structure. Proc. 11th ACM Conf. Electronic Commerce (Association for Computing Machinery, New York).Google Scholar
• [12] Chen HL, Roughgarden T (2009) Network design with weighted players. Theory Comput. Systems 45(2):302–324.Crossref, Google Scholar
• [13] Christodoulou G, Gairing M, Giannakopoulos Y, Poças D, Waldmann C (2020) Existence and complexity of approximate equilibria in weighted congestion games. Proc. 47th Internat. Colloquium Automata, Languages Programming (Schloss Dagstuhl, Wadern, Germany), 32:1–32:18.Google Scholar
• [14] Dafermos SC (1971) An extended traffic assignment model with applications to two-way traffic. Transportation Sci. 5(4):366–389.Link, Google Scholar
• [15] Dafermos SC (1972) The traffic assignment problem for multiclass-user transportation networks. Transportation Sci. 6(1):73–87.Link, Google Scholar
• [16] Dafermos SC (1980) Traffic equilibrium and variational inequalities. Transportation Sci. 14(1):42–54.Link, Google Scholar
• [17] Dafermos SC (1982) Relaxation algorithms for the general asymmetric traffic equilibrium problem. Transportation Sci. 16(2):231–240.Link, Google Scholar
• [18] Dunkel J, Schulz AS (2008) On the complexity of pure-strategy Nash equilibria in congestion and local-effect games. Math. Oper. Res. 33(4):851–868.Link, Google Scholar
• [19] Fabrikant A, Papadimitriou CH, Talwar K (2004) The complexity of pure Nash equilibria. Proc. 36th Annual ACM Sympos. Theory Comput. (Association for Computing Machinery, New York), 604–612.Google Scholar
• [20] Florian M (1977) A traffic equilibrium model of travel by car and public transit modes. Transportation Sci. 11(2):107–195.Link, Google Scholar
• [21] Florian M, Spiess H (1982) The convergence of diagonalization algorithms for asymmetric network equilibrium problems. Transportation Res. Part B: Methodological 16(6):477–483.Crossref, Google Scholar
• [22] Fotakis D, Kontogiannis S, Spirakis PG (2005) Selfish unsplittable flows. Theoret. Comput. Sci. 348(2–3):226–239.Crossref, Google Scholar
• [23] Friesz TL (1981) An equivalent optimization problem for combined multiclass distribution, assignment and modal split which obviates symmetry restrictions. Transportation Res. Part B: Methodological 15(5):361–369.Crossref, Google Scholar
• [24] Goemans MX, Mirrokni VS, Vetta A (2005) Sink equilibria and convergence. Proc. 46th Annual IEEE Sympos. Foundations Comput. Sci. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 142–154.Google Scholar
• [25] Gopalakrishnan R, Marden JR, Wierman A (2014) Potential games are necessary to ensure pure Nash equilibria in cost sharing games. Math. Oper. Res. 39(4):1252–1296.Link, Google Scholar
• [26] Hansknecht C, Klimm M, Skopalik A (2014) Approximate pure Nash equilibria in weighted congestion games. Proc. 17th Internat. Workshop Approximation Algorithms Combin. Optim. Problems (Schloss Dagstuhl, Wadern, Germany), 242–257.Google Scholar
• [27] Harks T, Klimm M (2012) On the existence of pure Nash equilibria in weighted congestion games. Math. Oper. Res. 37(3):419–436.Link, Google Scholar
• [28] Harks T, Klimm M (2016) Congestion games with variable demands. Math. Oper. Res. 41(1):255–277.Link, Google Scholar
• [29] Harks T, Klimm M, Möhring RH (2011) Characterizing the existence of potential functions in weighted congestion games. Theory Comput. Systems 49(1):46–70.Crossref, Google Scholar
• [30] Harks T, Klimm M, Möhring RH (2012) Strong equilibria in games with the lexicographical improvement property. Internat. J. Game Theory 42(2):461–482.Crossref, Google Scholar
• [31] Horni A, Nagel K, Axhausen KW, eds. (2016) The Multi-Agent Transport Simulation MATSim (Ubiquity Press, London).Crossref, Google Scholar
• [32] Kimber RM, McDonald M, Hounsell N (1985) Passenger car units in saturation flows: Concept, definition, derivation. Transportation Res. Part B: Methodological 19(1):39–61.Crossref, Google Scholar
• [33] Klimm M, Schütz A (2014) Congestion games with higher demand dimensions. Liu TY, Qi Q, Ye Y, eds. Web and Internet Economics. Lecture Notes in Computer Science, vol. 8877 (Springer, Cham, Switzerland), 453–459.Google Scholar
• [34] Kukushkin NS (2004) Acyclicity of improvements in games with common intermediate objectives. Working paper, Dorodnicyn Computing Center, Russian Academy of Sciences, Moscow.Google Scholar
• [35] Lam WHK, Huang HJ (1992) Calibration of the combined trip distribution and assignment model for multiple user classes. Transportation Res. Part B: Methodological 26(4):289–305.Crossref, Google Scholar
• [36] Lam WHK, Huang HJ (1992) A combined trip distribution and assignment model for multiple user classes. Transportation Res. Part B: Methodological 26(4):275–287.Crossref, Google Scholar
• [37] Libman L, Orda A (2001) Atomic resource sharing in noncooperative networks. Telecomm. Systems 17(4):385–409.Crossref, Google Scholar
• [38] Lu Z, Meng Q, Gomes G (2016) Estimating link travel time functions for heterogenous traffic flows on freeways. J. Advanced Transportation 50:1683–1698.Crossref, Google Scholar
• [39] Mahmassani HS, Mouskos KC (1988) Some numerical results on the diagonalization algorithm for network assignment with asymmetric interactions between cars and trucks. Transportation Res. Part B: Methodological 22(4):275–290.Crossref, Google Scholar
• [40] Marcotte P, Wynter L (2004) A new look at the multiclass network equilibrium problem. Transportation Sci. 38(3):282–292.Link, Google Scholar
• [41] Milchtaich I (1996) Congestion games with player-specific payoff functions. Games Econom. Behav. 13(1):111–124.Crossref, Google Scholar
• [42] Monderer D, Shapley LS (1996) Fictitious play property for games with identical interests. J. Econom. Theory 68(1):258–265.Crossref, Google Scholar
• [43] Monderer D, Shapley LS (1996) Potential games. Games Econom. Behav. 14(1):124–143.Crossref, Google Scholar
• [44] Noriega Y, Florian M (2007) Algorithmic approaches for asymmetric multi-class network equilibrium problems with different class delay relationships. Discussion Paper CIRRELT-2007-30, Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation, Montreal, Canada.Google Scholar
• [45] Panagopoulou PN, Spirakis PG (2006) Algorithms for pure Nash equilibria in weighted congestion games. ACM J. Experiment. Algorithmics 11:1–19.Google Scholar
• [46] Rosenthal RW (1973) A class of games possessing pure-strategy Nash equilibria. Internat. J. Game Theory 2(1):65–67.Crossref, Google Scholar
• [47] Rozenfeld O, Tennenholtz M (2006) Strong and correlated strong equilibria in monotone congestion games. Mavronicolas M, Kontogiannis S, eds. Internet and Network Economics. Lecture Notes in Computer Science, vol. 4286 (Springer, Berlin), 74–86.Google Scholar
• [48] Schmeidler D (1973) Equilibrium points of nonatomic games. J. Statist. Physics 7:295–300.Crossref, Google Scholar
• [49] Si B, Zhong M, Gao Z (2008) Link resistance function of urban mixed traffic network. J. Transportation Systems Engrg. Inform. Tech. 8(1):68–73.Crossref, Google Scholar
• [50] Smith MJ (1979) The existence, uniqueness and stability of traffic equilibria. Transportation Res. Part B: Methodological 13(4):295–304.Crossref, Google Scholar
• [51] Smock RJ (1962) An iterative assignment approach to capacity restraint on arterial networks. Highway Res. Board Bulletin 347:60–66.Google Scholar
• [52] Toint P, Wynter L (1996) Asymmetric multiclass assignment: A coherent formulation. Lesort JB, ed. Transportation Traffic Theory: Proc. 13th Internat. Sympos. Transportation Traffic Theory (Pergamon Press, Oxford, UK), 237–260.Google Scholar
• [53] U.S. Transportation Research Board (1965) Highway Capacity Manual, 1st ed. (National Academies of Sciences, Washington, DC).Google Scholar
• [54] Van Aerde M, Yagar S (1984) Capacity, speed, and platooning vehicle equivalents for two-lane rural highways. Transportation Res. Record 971:58–67.Google Scholar
• [55] Wardrop J (1952) Some theoretical aspects of road traffic research. Proc. Institution Civil Engineers 1(Part II):325–378.Crossref, Google Scholar