On the asymptotic behavior of the price of anarchy: Is selfish routing bad in highly congested networks?

This paper examines the asymptotic behavior of the price of anarchy as a function of the total traffic inflow in nonatomic congestion games with multiple origin-destination pairs. We first show that the price of anarchy may remain bounded away from 1, even in simple three-link parallel networks with convex cost functions. On the other hand, empirical studies show that the price of anarchy is close to 1 in highly congested real-world networks, thus begging the question: under what assumptions can this behavior be justified analytically? To that end, we prove a general result showing that for a large class of cost functions (defined in terms of regular variation and including all polynomials), the price of anarchy converges to 1 in the high congestion limit. In particular, specializing to networks with polynomial costs, we show that this convergence follows a power law whose degree can be computed explicitly.

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

[2]  Roberto Cominetti,et al.  On the Price of Anarchy of Highly Congested Nonatomic Network Games , 2016, SAGT.

[3]  Jeff S. Shamma,et al.  Risk Sensitivity of Price of Anarchy under Uncertainty , 2016, ACM Trans. Economics and Comput..

[4]  Thomas Mikosch,et al.  Regularly varying functions , 2006 .

[5]  Christos H. Papadimitriou,et al.  Worst-case Equilibria , 1999, STACS.

[6]  T. Roughgarden,et al.  Algorithmic Game Theory: Introduction to the Inefficiency of Equilibria , 2007 .

[7]  Mingyan Liu,et al.  Price of Anarchy for Congestion Games in Cognitive Radio Networks , 2012, IEEE Transactions on Wireless Communications.

[8]  H. Attouch.  Variational convergence for functions and operators , 1984 .

[9]  Georgios Piliouras,et al.  How bad is selfish routing in practice? , 2017, ArXiv.

[10]  Martin Gairing,et al.  Price of Anarchy for Polynomial Wardrop Games , 2006, WINE.

[11]  E.J. Friedman,et al.  Genericity and congestion control in selfish routing , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[12]  Michael Patriksson,et al.  Sensitivity Analysis of Traffic Equilibria , 2004, Transp. Sci..

[13]  Richard Cole,et al.  Large Market Games with Near Optimal Efficiency , 2016, EC.

[14]  Umang Bhaskar,et al.  Routing games , 2012 .

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

[16]  Michael T. Gastner,et al.  Price of anarchy in transportation networks: efficiency and optimality control. , 2007, Physical review letters.

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

[18]  Larry J. LeBlanc,et al.  AN EFFICIENT APPROACH TO SOLVING THE ROAD NETWORK EQUILIBRIUM TRAFFIC ASSIGNMENT PROBLEM. IN: THE AUTOMOBILE , 1975 .

[19]  Shaler Stidham,et al.  The Price of Anarchy for a Network of Queues in Heavy Traffic , 2014, Essays in Production, Project Planning and Scheduling.

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

[21]  David Watling,et al.  Mechanisms that Govern how the Price of Anarchy varies with Travel Demand , 2016 .

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

[23]  Dimitri P. Bertsekas,et al.  Data Networks , 1986 .

[24]  Sergio Grammatico,et al.  On the price of being selfish in large populations of plug-in electric vehicles , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

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

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

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

[28]  José R. Correa,et al.  Sloan School of Management Working Paper 4319-03 June 2003 Selfish Routing in Capacitated Networks , 2022 .

[29]  L. Haan,et al.  Extreme value theory : an introduction , 2006 .

[30]  Michael T. Gastner,et al.  The Price of Anarchy in Transportation Networks , 2007 .

[31]  José R. Correa,et al.  Fast, Fair, and Efficient Flows in Networks , 2007, Oper. Res..

[32]  Tim Roughgarden,et al.  The price of anarchy in large games , 2015, STOC.

[33]  Thomas Franke,et al.  Sensitivity of Wardrop Equilibria , 2010, Theory of Computing Systems.

[34]  S. Resnick.  Heavy-Tail Phenomena: Probabilistic and Statistical Modeling , 2006 .

[35]  J. Karamata,et al.  Sur un mode de croissance régulière. Théorèmes fondamentaux , 1933 .

[36]  Yanyan Chen,et al.  Selfishness need not be bad , 2017, ArXiv.

[37]  Luis Alcalá.  On the relation between regular variation and the asymptotic elasticity of substitution , 2014 .

[38]  José R. Correa,et al.  A Geometric Approach to the Price of Anarchy in Nonatomic Congestion Games , 2008, Games Econ. Behav..