A set of parallel jobs must be scheduled in a grid, which has multi clusters that consist of many identical processors, to minimize the global objective function, the makespan. A parallel job requires several processors for simultaneously executing and it needs some unit times to finish its execution. In practice, each parallel job is owned by an independent agent, which is selfish and select a cluster to minimize its own completion time. This scenario can be represented as a coordination mechanism game, in which the players are job owners, and the strategies are the clusters, and the player’s disutility is the completion time of its job in the corresponding schedule.
In this work, we design and analyze coordination mechanisms for machines, which aim to minimize the price of anarchy. We study two classes of scheduling policies, the Bottom-Left based algorithms and the Shelf-Packing based algorithms, both in a homogeneous grid and in a heterogeneous grid. We derive upper and lower bounds on the price of anarchy of these coordination mechanisms. We also show that such games are potential games that converge in a linear number of rounds.