Models of Non-atomic Congestion Games - From Unicast to Multicast Routing

We give an overview of important results for non-atomic congestion games in their traditional form along with self-contained and short proofs and then present new results and challenges for an extended model, which we call consumption-relevance congestion games . We introduce the consumption-relevance congestion game first and show that all other models are special cases of it. Our focus is on the price of anarchy, computation of equilibria, and experimental studies. Further interesting aspects are summarized at the end of this article.

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

[2]  Steve Chien,et al.  Convergence to approximate Nash equilibria in congestion games , 2007, SODA '07.

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

[4]  Anna Nagurney,et al.  On a Paradox of Traffic Planning , 2005, Transp. Sci..

[5]  D. Kinderlehrer,et al.  An introduction to variational inequalities and their applications , 1980 .

[6]  Lasse Kliemann,et al.  The Price of Anarchy and Computation of Equilibria in Non-atomic Consumption-Relevance Congestion Games , 2008 .

[7]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[8]  Berthold Vöcking,et al.  Fast convergence to Wardrop equilibria by adaptive sampling methods , 2006, STOC '06.

[9]  Tim Roughgarden,et al.  Selfish Routing , 2002 .

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

[11]  Berthold Vöcking,et al.  Approximating Wardrop Equilibria with Finitely Many Agents , 2007, DISC.

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

[13]  Anand Srivastav,et al.  The Price of Anarchy in Selfish Multicast Routing , 2006, CAAN.

[14]  Nicholas I. M. Gould,et al.  Lancelot: A FORTRAN Package for Large-Scale Nonlinear Optimization (Release A) , 1992 .

[15]  J. Wardrop ROAD PAPER. SOME THEORETICAL ASPECTS OF ROAD TRAFFIC RESEARCH. , 1952 .

[16]  Ariel Orda,et al.  Achieving network optima using Stackelberg routing strategies , 1997, TNET.

[17]  A. Nagurney Network Economics: A Variational Inequality Approach , 1992 .

[18]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

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

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

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

[22]  Jeannette Janssen,et al.  Combinatorial and Algorithmic Aspects of Networking, 4th Workshop, CAAN 2007, Halifax, Canada, August 14, 2007. Revised Papers , 2007, CAAN.

[23]  Mohammad Mahdian,et al.  Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games , 2004, 45th Annual IEEE Symposium on Foundations of Computer Science.