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We introduce the concept of resource management for in-network caching environments. We argue that in Information-Centric Networking environments, deterministically caching content messages at predefined places along the content delivery path results in unfair and inefficient content multiplexing between different content flows. Instead, introducing sophisticated mechanisms to allocate resources along the path according to content flow characteristics results in better use of network resources and therefore, higher overall performance. We depart from the observation that caching every content message at every router that this message traverses causes huge caching redundancy in Information-Centric Networks. We call this scheme Cache Everything - Everywhere (CE2) and try to find alternative in-network caching schemes that reduce caching redundancy and in turn, result in better resource utilisation. The design principles of our proposed in-network caching scheme, which we call ProbCache, target these two outcomes, namely reduction of caching redundancy and fair content flow multiplexing along the delivery path. In particular, ProbCache approximates the caching capability of a path and caches contents probabilistically to: i) leave caching space for other flows sharing (part of) the same path, and ii) fairly multiplex contents in caches along the path from the server to the client. We evaluate the proposed schemes in both homogeneous and heterogeneous cache size environments and formulate a framework for resource allocation in in-network caching environments. The proposed probabilistic approach to in-network caching exhibits ideal performance both in terms of network resource utilisation and in terms of resource allocation fairness among competing content flows.