Resource-Aware Cost-Sharing Methods for Scheduling Games

In large distributed systems, ensuring the efficient utilization of the available resources is a very challenging task. Given limited information regarding the state of the system and no centralized control over the outcome, decentralized scheduling mechanisms are unable to enforce optimal utilization. To better understand such systems, some classic papers that introduced game theoretic models used the “price of anarchy” measure to evaluate the system’s performance. The paper “Resource-Aware Cost-Sharing Methods for Scheduling Games” by Christodoulou, Gkatzelis, and Sgouritsa overcomes some of the overly pessimistic results shown in this prior work by enhancing the scheduling mechanisms with access to some additional information regarding the state of the system: a “resource-aware” mechanism knows what machines are available in the system and uses this information to carefully incentivize the users toward more efficient Nash equilibrium outcomes. We study the performance of cost-sharing methods in a selfish scheduling setting where a group of users schedule their jobs on machines with load-dependent cost functions, aiming to minimize their own cost. Anticipating this user behavior, the system designer chooses a decentralized protocol that defines how the cost generated on each machine is to be shared among its users, and the performance of the protocol is evaluated over the Nash equilibria of the induced game. Previous work on selfish scheduling has focused on two extreme models: omniscient protocols that are aware of every machine and every job that is active at any given time, and oblivious protocols that are aware of nothing beyond the machine they control. We focus on a well-motivated middle-ground model of resource-aware protocols, which are aware of the set of machines in the system, but unaware of what jobs are active at any given time. Furthermore, we study the extent to which appropriately overcharging the users can lead to improved performance. We provide protocols that achieve small constant price of anarchy bounds when the cost functions are convex or concave, and we complement our positive results with impossibility results for general cost functions. Funding: This work was supported by the Royal Society [Grant LT140046], the Engineering and Physical Sciences Research Council [Grant EP/M008118/1], the National Science Foundation [Grants CCF-1161813, CCF-1216073, and CCF-1408635; CAREER Award CCF-2047907], and the Lise Meitner Award Fellowship.