A decentralized game theoretic framework applied to Web caching is discussed. The interaction of multiple clients with a caching server is modeled as a noncooperative game, in which clients are viewed as players, and the caching server disk space as a resource for which players are competing. However, some clients may continuously request new objects, thus, occupying a considerable portion of the cache disk, enjoying high hit rates. Such an aggressive behavior may have significant impact to the overall cache performance, as few clients may monopolize the total disk space, and the remaining clients may suffer the eviction of their "important" resources from the cache, thus, experiencing numerous cache misses. Moreover, it is observed that the majority of hits in cache systems are due to shared objects, i.e., clients tend to refer to a "pool" of common resources. The objective of the proposed framework is to discourage monopolizing the cache disk space by a minority of clients, while rewarding clients that contribute to the overall hit rate. The efficiency of the proposed scheme is evaluated through simulations.