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Resource allocation involves deciding how to divide a resource of limited availability across multiple demands in a way that optimizes current objectives (e.g., allocating a processor's computing resources to the demand presented by tasks in order to maximize task completion throughput). In "distributed" resource allocation there are multiple resource types each of which can be subdivided, but then each can only be allocated to a subset of the demands (e.g., in a multiprocessor system where each processor can only process certain task types). In this paper we focus on one type of cooperative resource allocation problem where via an imperfect communication network multiple processors can share the workload presented by multiple task types. We introduce asynchronous "cooperative" resource allocation strategies, and show that they lead to the cumulative demand being bounded by a constant. We demonstrate via simulations when they might be superior to one noncooperative strategy.