Tighter Bounds on the Inefficiency Ratio of Stable Equilibria in Load Balancing Games

TL;DR

This paper establishes tighter bounds on the inefficiency ratio of stable equilibria in load balancing games, improving the understanding of how equilibrium solutions compare to optimal load distributions.

Contribution

It provides new lower and upper bounds of 7/6 and 4/3, refining previous bounds for the inefficiency ratio in load balancing games.

Findings

Lower bound of 7/6 for inefficiency ratio

Upper bound of 4/3 for inefficiency ratio

Results also apply to $L_2$-norm approximation of $L_{ ext{infinity}}$-norm in scheduling

Abstract

In this paper we study the inefficiency ratio of stable equilibria in load balancing games introduced by Asadpour and Saberi [3]. We prove tighter lower and upper bounds of 7/6 and 4/3, respectively. This improves over the best known bounds in problem (19/18 and 3/2, respectively). Equivalently, the results apply to the question of how well the optimum for the $L_2$ -norm can approximate the $L_{\infty}$-norm (makespan) in identical machines scheduling.