How Hard Is It to Find Extreme Nash Equilibria in Network Congestion Games?

We study the complexity of finding extreme pure Nash equilibria in symmetric (unweighted) network congestion games. In our context best and worst equilibria are those with minimum respectively maximum makespan. On series-parallel graphs a worst Nash equilibrium can be found by a Greedy approach while finding a best equilibrium is NP-hard. For a fixed number of users we give a pseudo-polynomial algorithm to find the best equilibrium in series-parallel networks. For general network topologies also finding a worst equilibrium is NP-hard.

[1]  Peter Brucker,et al.  Minimum cost flow algorithms for series-parallel networks , 1985, Discret. Appl. Math..

[2]  Gerhard J. Woeginger,et al.  How hard is it to find extreme Nash equilibria in network congestion games? , 2009, Theor. Comput. Sci..

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

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

[5]  Yishay Mansour,et al.  Efficient graph topologies in network routing games , 2009, Games Econ. Behav..

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

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

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

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

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

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

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

[13]  Martin Gairing,et al.  Nashification and the Coordination Ratio for a Selfish Routing Game , 2003, ICALP.

[14]  Christos H. Papadimitriou,et al.  The complexity of pure Nash equilibria , 2004, STOC '04.

[15]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[16]  Paul G. Spirakis,et al.  Structure and complexity of extreme Nash equilibria , 2005, Theor. Comput. Sci..

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

[18]  Berthold Vöcking,et al.  On the structure and complexity of worst-case equilibria , 2007, Theor. Comput. Sci..

[19]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

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