We consider the problem of efficient content delivery over networks in which individual nodes are equipped with content caching capabilities. We present a flexible methodology for the design of cooperative, decentralized caching strategies that can adapt to real-time changes in regional content popularity. This design methodology makes use of a recently proposed reduced consensus optimization scheme, in which a number of networked agents cooperate in locating the optimum of the sum of their individual, privately known objective functions. The outcome of the design is a set of dynamic update rules that stipulate how much and which portions of each content piece an individual network node ought to cache. In implementing these update rules, the nodes achieve a collectively optimal caching configuration through nearest-neighbor interactions and measurements of local content request rates only. Moreover, individual nodes need not be aware of the overall network topology or how many other nodes are on the network. The desired caching behavior is encoded in the design of individual nodes' costs and can incorporate a variety of network performance criteria. Using the proposed methodology, we develop a set of content-caching update rules designed to minimize the energy consumption of the network as a whole by dynamically trading off transport and caching energy costs in response to changes in content demand.