Tradeoffs in Worst-Case Equilibria

Abstract

We investigate the problem of routing traffic through a congested network in an environment of non-cooperative users. We use the worst-case coordination ratio suggested by Koutsoupias and Papadimitriou to measure the performance degradation due to the lack of a centralized traffic regulating authority. We provide a full characterization of the worst-case coordination ratio in the restricted assignment and unrelated parallel links model. In particular, we quantify the tradeoff between the "negligibility" of the traffic controlled by each user and the worst-case coordination ratio. We analyze both pure and mixed strategies systems and identify the range where their performance is similar.

Strong price of anarchy

“…equilibrium, and thus the strong price of stability is 1. As for the strong price of anarchy, while it is rather simple to show that for unrelated machines the PoA is unbounded (Awerbuch et al, 2006), we show that the SPoA is bounded as a function of the number of players and machines. More specifically, we show that 7 :…”

“…For identical machines, it is known that PoA 2 (Koutsoupias and Papadimitriou, 1999), while for unrelated machines, the PoA may be unbounded (Awerbuch et al, 2006). Consider the following motivating example for unrelated machines.…”

Strong equilibrium in cost sharing connection games

“…Papadimitriou (2001) and Koutsoupias and Papadimitriou (1999) coined the term price of anarchy (PoA), referring to the ratio between the cost of the worst-case Nash equilibrium and the optimal solution. This notion has been extensively studied in various settings, including job scheduling (Koutsoupias and Papadimitriou, 1999;Christodoulou et al, 2004;Czumaj and Vöcking, 2002;Awerbuch et al, 2003), network design (Albers et al, 2006;Anshelevich et al, 2004Anshelevich et al, , 2003Fabrikant et al, 2003), network routing (Roughgarden and Tardos, 2002;Roughgarden, 2002;Awerbuch et al, 2005;Christodoulou and Koutsoupias, 2005) and more. Similarly, Andelman et al (2007) defined the strong price of anarchy (SPoA) as the ratio between the cost of the worst-case strong equilibrium and the optimal solution.…”

Greedy distributed optimization of multi-commodity flows

“…A popular approach in economics, and more recently, in theoretical computer science [24,34,2,3,11,31] is to focus on the issue of quality of Nash equilibria, e.g., analyzing "price of anarchy". If each agent is responsible for an infinitesimal amount of flow, then the rerouting along shorter paths decreases the natural potential function, thus causing (eventual) convergence to (approximate) Nash equilibrium, potentially after a long time.…”