Exact Price of Anarchy for Polynomial Congestion Games

We show exact values for the worst-case price of anarchy in weighted and unweighted (atomic unsplittable) congestion games, provided that all cost functions are bounded-degree polynomials with nonnegative coefficients. The given values also hold for weighted and unweighted network congestion games.

[1]  Yossi Azar,et al.  The Price of Routing Unsplittable Flow , 2005, STOC '05.

[2]  José R. Correa,et al.  The Impact of Oligopolistic Competition in Networks , 2009, Oper. Res..

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

[4]  Max Klimm,et al.  On the Existence of Pure Nash Equilibria in Weighted Congestion Games , 2010, Math. Oper. Res..

[5]  I. Milchtaich,et al.  Congestion Games with Player-Specific Payoff Functions , 1996 .

[6]  Tim Roughgarden,et al.  Selfish routing and the price of anarchy , 2005 .

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

[8]  Paul G. Spirakis,et al.  Selfish unsplittable flows , 2005, Theor. Comput. Sci..

[9]  Ariel Orda,et al.  Atomic Resource Sharing in Noncooperative Networks , 1997, Proceedings of INFOCOM '97.

[10]  Georgia Perakis,et al.  The "Price of Anarchy" Under Nonlinear and Asymmetric Costs , 2007, Math. Oper. Res..

[11]  Martin Gairing,et al.  Total Latency in Singleton Congestion Games , 2007, WINE.

[12]  Elias Koutsoupias,et al.  On the Price of Anarchy and Stability of Correlated Equilibria of Linear Congestion Games , 2005, ESA.

[13]  Tobias Harks Stackelberg Strategies and Collusion in Network Games with Splittable Flow , 2008, WAOA.

[14]  Elias Koutsoupias,et al.  The price of anarchy of finite congestion games , 2005, STOC '05.

[15]  R. Aumann Subjectivity and Correlation in Randomized Strategies , 1974 .

[16]  Martin Gairing,et al.  Exact Price of Anarchy for Polynomial Congestion Games , 2006, STACS.

[17]  Tim Roughgarden,et al.  How unfair is optimal routing? , 2002, SODA '02.

[18]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

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

[20]  Paul G. Spirakis,et al.  Symmetry in Network Congestion Games: Pure Equilibria and Anarchy Cost , 2005, WAOA.

[21]  Berthold Vöcking,et al.  Selfish traffic allocation for server farms , 2002, STOC '02.

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

[23]  Eric van Damme,et al.  Non-Cooperative Games , 2000 .

[24]  Marios Mavronicolas,et al.  The price of anarchy for polynomial social cost , 2004, Theor. Comput. Sci..

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

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

[27]  Tobias Harks,et al.  Stackelberg Strategies and Collusion in Network Games with Splittable Flow , 2009, Theory of Computing Systems.

[28]  H. Peyton Young,et al.  Strategic Learning and Its Limits , 2004 .

[29]  J. Nash Equilibrium Points in N-Person Games. , 1950, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Marios Mavronicolas,et al.  A new model for selfish routing , 2004, Theor. Comput. Sci..

[31]  Yossi Azar,et al.  Tradeoffs in worst-case equilibria , 2003, Theor. Comput. Sci..

[32]  Berthold Vöcking,et al.  Tight bounds for worst-case equilibria , 2002, SODA '02.

[33]  Marios Mavronicolas,et al.  Nash Equilibria in Discrete Routing Games with Convex Latency Functions , 2004, ICALP.

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

[35]  Dimitris Fotakis Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy , 2009, Theory of Computing Systems.

[36]  A. Mas-Colell,et al.  Microeconomic Theory , 1995 .

[37]  Martin Gairing,et al.  Selfish Routing with Incomplete Information , 2005, SPAA '05.

[38]  Mohammad Taghi Hajiaghayi,et al.  Regret minimization and the price of total anarchy , 2008, STOC.

[39]  L. Shapley,et al.  Potential Games , 1994 .

[40]  Tim Roughgarden,et al.  Local smoothness and the price of anarchy in atomic splittable congestion games , 2011, SODA '11.

[41]  R. Rosenthal A class of games possessing pure-strategy Nash equilibria , 1973 .

[42]  R. McKelvey,et al.  Computation of equilibria in finite games , 1996 .

[43]  Martin Gairing,et al.  Nash Equilibria, the Price of Anarchy and the Fully Mixed Nash Equilibrium Conjecture , 2005, ICALP.

[44]  Paul G. Spirakis,et al.  Approximate Equilibria and Ball Fusion , 2003, Theory of Computing Systems.