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Although cooperation generally increases the amount of resources available to a community of nodes, thus improving individual and collective performance, it also allows for the appearance of potential mistreatment problems through the exposition of one node's resources to others. We study such concerns by considering a group of independent, rational, self-aware nodes that cooperate using online caching algorithms, where the exposed resource is the storage at each node. Motivated by content networking applications - including Web caching, content delivery networks (CDNs), and peer-to-peer (P2P) - this paper extends our previous work on the offline version of the problem, which was conducted under a game-theoretic framework and limited to object replication. We identify and investigate two causes of mistreatment: 1) cache state interactions (due to the cooperative servicing of requests) and 2) the adoption of a common scheme for cache management policies. Using analytic models, numerical solutions of these models, and simulation experiments, we show that online cooperation schemes using caching are fairly robust to mistreatment caused by state interactions. To appear in a substantial manner, the interaction through the exchange of miss streams has to be very intense, making it feasible for the mistreated nodes to detect and react to exploitation. This robustness ceases to exist when nodes fetch and store objects in response to remote requests, that is, when they operate as level-2 caches (or proxies) for other nodes. Regarding mistreatment due to a common scheme, we show that this can easily take place when the "outlier" characteristics of some of the nodes get overlooked. This finding underscores the importance of allowing cooperative caching nodes the flexibility of choosing from a diverse set of schemes to fit the peculiarities of individual nodes. To that end, we outline an emulation-based framework for the development of mistreatment-resilient distributed selfis- h caching schemes.