The Price of Anarchy for the Load Balancing Game with a Randomizing Scheduler

Abstract

We study the price of anarchy (PoA) for the load balancing game with a randomizing scheduler. Given a system of facilities and players, each facility is associated with a linear cost function, while all players are in an ordering randomly taken by a scheduler, from the set of permutations of all players. Each player chooses exactly one of these facilities to fulfill his task, which incurs to him a cost depending on not only the facility he chooses but also his position in the ordering. In competing for the facility usage, each player tries to optimize his own objective determined by a certain decision-making principle. On the other hand, for balancing the load, it is desirable to minimize the maximum cost of all players. Concerning this system goal of load balance, we estimate the PoAs of this class of games, provided all players follow one of the four decision-making principles, namely the bottom-out, win-or-go-home, average-case-analysis, and minimax-regret principles.