Tight bounds for worst-case equilibria

The coordination ratio is a game theoretic measure that aims to reflect the price of selfish routing in a network. We show the worst-case coordination ratio on m parallel links (of possibly different speeds) isΘ(log m/log log log m)Our bound is asymptotically tight and it entirely resolves an question posed recently by Koutsoupias and Papadimitriou [3].

[1]  Mihalis Yannakakis,et al.  On complexity as bounded rationality (extended abstract) , 1994, STOC '94.

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

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

[4]  W. Hoeffding.  Probability inequalities for sum of bounded random variables , 1963 .

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

[6]  N. Fisher,et al.  Probability Inequalities for Sums of Bounded Random Variables , 1994 .

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

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

[9]  Christos H. Papadimitriou,et al.  Game theory and mathematical economics: a theoretical computer scientist's introduction , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[10]  J. Nash.  NON-COOPERATIVE GAMES , 1951, Classics in Game Theory.

[11]  Gaston H. Gonnet,et al.  Expected Length of the Longest Probe Sequence in Hash Code Searching , 1981, JACM.

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

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

[14]  Paul G. Spirakis,et al.  The price of selfish routing , 2001, STOC '01.

[15]  P. Gács,et al.  Algorithms , 1992 .

[16]  Paul G. Spirakis,et al.  The structure and complexity of Nash equilibria for a selfish routing game , 2002, Theor. Comput. Sci..