The efficiency of Nash equilibria in the load balancing game with a randomizing scheduler.

• We study a load balancing game with uncertainty imposed by a randomizing scheduler. • We provide nearly tight upper bounds on PoAs when players follow the win-or-go-home and minimum-expected-cost principles. • The bottom-out principle is studied for the first time in load balancing games. • Non-optimal prices of stabilities exhibit a sharp contrast with the classical load balancing games. We study the efficiency of Nash equilibria for the load balancing game with a randomizing scheduler. In the game, we are given a set of facilities and a set of players along with a scheduler, where each facility is associated with a linear cost function, and the players are randomly ordered by the scheduler. Each player chooses exactly one of these facilities to fulfill his task, which incurs to him a cost depending on not only the cost function of the facility he chooses and the players who choose the same facility (as in a usual load balancing game), but also his uncertain position in the uniform random ordering. From an individual perspective, each player tries to choose a facility for optimizing his own objective that is determined by a certain decision-making principle. From a system perspective, it is desirable to minimize the maximum cost among all players, which is a commonly used criterion for load balancing. We estimate the price of anarchy and price of stability for this class of load balancing games under uncertainty, provided all players follow one of the four decision-making principles, namely the bottom-out, win-or-go-home, minimum-expected-cost, and minimax-regret principles. Our results show that the efficiency loss of Nash equilibria in these decentralized environments heavily rely on player's attitude toward the uncertainty. [ABSTRACT FROM AUTHOR]