Bottleneck Routing Games with Low Price of Anarchy

TL;DR

This paper introduces exponential bottleneck routing games that significantly reduce the inefficiency of Nash equilibria, achieving a poly-logarithmic bound on the price of anarchy in network congestion scenarios.

Contribution

The paper proposes exponential utility functions in bottleneck routing games, resulting in a much lower price of anarchy compared to traditional models.

Findings

Exponential bottleneck games have a poly-logarithmic price of anarchy bound.

Adjusting utility costs with a logarithm retains similar player costs to traditional bottleneck games.

Exponential utility functions improve efficiency of equilibria in network routing.

Abstract

We study {\em bottleneck routing games} where the social cost is determined by the worst congestion on any edge in the network. In the literature, bottleneck games assume player utility costs determined by the worst congested edge in their paths. However, the Nash equilibria of such games are inefficient since the price of anarchy can be very high and proportional to the size of the network. In order to obtain smaller price of anarchy we introduce {\em exponential bottleneck games} where the utility costs of the players are exponential functions of their congestions. We find that exponential bottleneck games are very efficient and give a poly-log bound on the price of anarchy: $O(\log L \cdot \log |E|)$, where $L$ is the largest path length in the players' strategy sets and $E$ is the set of edges in the graph. By adjusting the exponential utility costs with a logarithm we obtain games whose player costs are almost identical to those in regular bottleneck games, and at the same time have the good price of anarchy of exponential games.