Abstract

Suppose that a set of weighted tasks shall be assigned to a set of machines with possibly different speeds such that the load is distributed evenly among the machines. In computer science, this problem is traditionally treated as an optimization problem. One of the classical objectives is to minimize the makespan, i.e., the maximum load over all machines. Here we study a natural game theoretic variant of this problem: We assume that the tasks are managed by selfish agents, i.e., each task has an agent that aims at placing the task on the machine with smallest load. We study the Nash equilibria of this game and compare them with optimal solutions with respect to the makespan. The ratio between the worst-case makespan in a Nash equilibrium and the optimal makespan is called the price of anarchy. In this chapter, we study the price of anarchy for such load balancing games in four different variants, and we investigate the complexity of computing equilibria.

Introduction

The problem of load balancing is fundamental to networks and distributed systems. Whenever a set of tasks should be executed on a set of resources, one needs to balance the load among the resources in order to exploit the available resources efficiently. Often also fairness aspects have to be taken into account. Load balancing has been studied extensively and in many variants.