Multimedia content distribution through a distributed system, a
peer-to-peer (P2P) network for instance, is attractive since it
harnesses the resources available with the numerous peers in the
network. Another advantage of such a system is that the potentially
available resources scale in proportion to the demand as more and more peers join the system. Recent studies have concentrated mainly on such aspects of these distributed networks as querying, indexing, etc. These studies however take for granted the voluntary contribution of resources by peers in the system. Empirical evidence however points to the contrary, <i>i.e.</i> in existing P2P systems, a substantial fraction of peers do not contribute resources to the system, while benefiting from the services it provides at the expense of the contributing peers. In this paper we analyze a P2P system in a game-theoretic setting in which games involving content exchange are played repeatedly. The model takes into account the manner in which a peer adapts his contribution to the system depending on the benefit he has derived from the system so far and expects to derive in the long run. The model enables us to formulate an optimization problem that ields optimal content sharing trategies that a peer should adopt in rder to maximize his net benefit by participating in the system.