The Impact of Exponential Utility Costs in Bottleneck Routing Games

TL;DR

This paper introduces exponential bottleneck routing games, demonstrating that they significantly improve efficiency with a poly-logarithmic bound on the price of anarchy compared to traditional bottleneck games.

Contribution

The paper proposes exponential utility functions in bottleneck routing games, achieving a poly-logarithmic bound on the price of anarchy, which is a substantial improvement over previous models.

Findings

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

Traditional bottleneck games can have very high inefficiency.

Exponential utility functions lead to more efficient equilibria.

Abstract

We study bottleneck routing games where the social cost is determined by the worst congestion on any edge in the network. Bottleneck games have been studied in the literature by having the player's utility costs to be 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 with respect to the parameters of the game. In order to obtain smaller price of anarchy we explore {\em exponential bottleneck games} where the utility costs of the players are exponential functions on the congestion of the edges in their paths. We find that exponential bottleneck games are very efficient giving a poly-log bound on the price of anarchy: O(log L log |E|), where L is the largest path length in the players strategy sets and E is the set of edges in the graph.