The Price of Anarchy for Selfish Ring Routing is Two

TL;DR

This paper establishes that in selfish ring routing with linear link latencies, the worst-case inefficiency (price of anarchy) for maximum latency is exactly two, providing a precise bound for this social cost measure.

Contribution

It proves a tight upper bound of two on the price of anarchy for maximum latency in selfish ring routing with linear latencies, a previously less understood social cost.

Findings

Price of anarchy is at most two for the maximum latency in the specified setting.

The bound of two is tight, meaning it cannot be improved.

First sharp bound for the maximum latency social cost in this context.

Abstract

We analyze the network congestion game with atomic players, asymmetric strategies, and the maximum latency among all players as social cost. This important social cost function is much less understood than the average latency. We show that the price of anarchy is at most two, when the network is a ring and the link latencies are linear. Our bound is tight. This is the first sharp bound for the maximum latency objective.