Sloan School of Management Working Paper 4319-03 June 2003 Selfish Routing in Capacitated Networks

According to Wardrop's first principle, agents in a congested network choose their routes selfishly, a behavior that is captured by the Nash equilibrium of the underlying noncooperative game. A Nash equilibrium does not optimize any global criterion per se, and so there is no apparent reason why it should be close to a solution of minimal total travel time, i.e., the system optimum. In this paper, we offer positive results on the efficiency of Nash equilibria in traffic networks. In contrast to prior work, we present results for networks with capacities and for latency functions that are nonconvex, nondifferentiable, and even discontinuous.The inclusion of upper bounds on arc flows has early been recognized as an important means to provide a more accurate description of traffic flows. In this more general model, multiple Nash equilibria may exist and an arbitrary equilibrium does not need to be nearly efficient. Nonetheless, our main result shows that the best equilibrium is as efficient as in the model without capacities. Moreover, this holds true for broader classes of travel cost functions than considered hitherto.

[1]  J. Kohl.  Der Verkehr und die Ansiedelungen der Menschen in ihrer Abhängigkeit von der Gestaltung der Erdoberfläche , 1850 .

[2]  A. C. Pigou.  Economics of welfare , 1920 .

[3]  F. Knight.  Some Fallacies in the Interpretation of Social Cost , 1924 .

[4]  J. G. Wardrop,et al.  Some Theoretical Aspects of Road Traffic Research , 1952 .

[5]  T. Koopmans,et al.  Studies in the Economics of Transportation. , 1956 .

[6]  A Downs,et al.  THE LAW OF PEAK-HOUR EXPRESSWAY CONGESTION , 1962 .

[7]  Niels O Jorgensen,et al.  Some aspects of the urban traffic assignment problem , 1963 .

[8]  Dietrich Braess,et al.  Über ein Paradoxon aus der Verkehrsplanung , 1968, Unternehmensforschung.

[9]  Stella C. Dafermos,et al.  Traffic assignment problem for a general network , 1969 .

[10]  Peter A. Steenbrink,et al.  Optimization of Transport Networks , 1974 .

[11]  David Branston,et al.  LINK CAPACITY FUNCTIONS: A REVIEW , 1976 .

[12]  C. Daganzo.  On the traffic assignment problem with flow dependent costs—II , 1977 .

[13]  Deepak K. Merchant,et al.  A Model and an Algorithm for the Dynamic Traffic Assignment Problems , 1978 .

[14]  Mike Smith,et al.  The existence, uniqueness and stability of traffic equilibria , 1979 .

[15]  Stanley B. Gershwin,et al.  Pilot study of computer-based urban traffic management , 1980 .

[16]  Stella Dafermos,et al.  Traffic Equilibrium and Variational Inequalities , 1980 .

[17]  D. Hearn,et al.  Convergence of the Frank-Wolfe method for certain bounded variable traffic assignment problems , 1981 .

[18]  David E. Boyce,et al.  The effect on equilibrium trip assignment of different link congestion functions , 1981 .

[19]  T. Magnanti.  MODELS AND ALGORITHMS FOR PREDICTING URBAN TRAFFIC EQUILIBRIA , 1984 .

[20]  Susan Powell,et al.  Transportation Planning Models , 1987 .

[21]  David E. Boyce,et al.  Contributions of Transportation Network Modeling to the Development of a Real-Time Route Guidance System , 1989 .

[22]  A. Nagurney.  Migration equilibrium and variational inequalities. , 1989, Economics letters.

[23]  Jean-Loup Farges,et al.  Route Guidance, Individual , 1991 .

[24]  M. Papageorgiou,et al.  Concise encyclopedia of traffic & transportation systems , 1991 .

[25]  Hai Yang,et al.  Traffic Assignment and Traffic Control in General Freeway-arterial Corridor Systems , 1994 .

[26]  David Bernstein,et al.  Equilibria for Networks with Lower Semicontinuous Costs: With an Application to Congestion Pricing , 1994, Transp. Sci..

[27]  M. Patriksson,et al.  An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems , 1995 .

[28]  M. Patriksson,et al.  Equilibrium characterizations of solutions to side constrained asymmetric traffic assignment models , 1995 .

[29]  D. Hearn,et al.  Solving Congestion Toll Pricing Models , 1998 .

[30]  A. Palma,et al.  Optimization formulations and static equilibrium in congested transportation networks , 1998 .

[31]  Torbjörn Larsson,et al.  Side constrained traffic equilibrium models: analysis, computation and applications , 1999 .

[32]  Tim Roughgarden,et al.  How bad is selfish routing? , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[33]  Christos H. Papadimitriou,et al.  Algorithms, games, and the internet , 2001, STOC '01.

[34]  Christos H. Papadimitriou,et al.  Algorithms, Games, and the Internet , 2001, ICALP.

[35]  Tim Roughgarden,et al.  The price of anarchy is independent of the network topology , 2002, STOC '02.

[36]  Kwang Mong Sim,et al.  The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands , 2003, Oper. Res. Lett..

[37]  Tim Roughgarden.  The price of anarchy is independent of the network topology , 2003, J. Comput. Syst. Sci..

[38]  Patrice Marcotte,et al.  A Strategic Flow Model of Traffic Assignment in Static Capacitated Networks , 2004, Oper. Res..

[39]  Tim Roughgarden,et al.  Bounding the inefficiency of equilibria in nonatomic congestion games , 2004, Games Econ. Behav..

[40]  G. Perakis,et al.  The Price of Anarchy when Costs Are Non-separable and Asymmetric , 2004, IPCO.

[41]  Andreas S. Schulz,et al.  Selfish versus coordinated routing in network games , 2004 .

[42]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .