In this paper, we study the cooperative games between companies that pool their spare part inventory to maintain their equipment. Due to the high cost of service disruptions, any stockout is assumed to be satisfied by an expedited delivery. We firstly derive the performance measures used to formulate the long run average cost of running these spare parts systems and show that, in the long run, these performance measures are equivalent to those in classical spare parts system with backlogs. Afterwards, we show that the core of these games are non-empty by showing that proportional allocation is a population monotonic allocation scheme.