ABSTRACT Stackelberg Scheduling Strategies

We study the problem of optimizing the performance of a system shared by selfish, noncooperative users. We consider the concrete setting of scheduling jobs on a set of shared machines with load-dependent latency functions specifying the length of time necessary to complete a job; we measure system performance by the total latency of the system. Assigning jobs according to the selfish interests of individual users (who wish to minimize only the latency that their own jobs experience) typically results in suboptimal system performance. However, in many systems of this type there is a mixture of “selfishly controlled ” and “centrally controlled” jobs; as the assignment of centrally controlled jobs will influence the subsequent actions by selfish users, we aspire to contain the degradation in system performance due to selfish behavior by scheduling the centrally controlled jobs in the best possible way. We formulate this goal as an optimization problem via Stackelberg games, games in which one player acts a leader (here, the centralized authority interested in optimizing system performance) and the rest as followers (the selfish users). The problem is then to compute a strategy for the leader (a Stackelberg strategy) that induces the followers to react in a way that (at least approximately) minimizes the total latency in the system. In this paper, we prove that it is NP-hard to compute the optimal Stackelberg strategy and present simple strategies with provable performance guarantees. More precisely, we give a simple algorithm that computes a strategy inducing a job assignment with total latency no more than a constant times that of the optimal assignment of all of the jobs; in the absence of centrally controlled jobs and a Stackelberg strategy, no result of this type is possible. We also prove stronger performance guarantees in the special case where every machine latency function is linear in the machine load