We study the interaction among users of unstructured file sharing applications, who compete for available network resources (link bandwidth or capacity) by opening multiple connections on multiple paths so as to accelerate data transfer. We model this interaction with an unstructured file sharing game. Users are players and their strategies are the numbers of sessions on available paths. We consider a general bandwidth sharing framework proposed by Kelly [1] and Mo and Walrand [2], with TCP as a special case. Furthermore, we incorporate the Tit-for-Tat strategy (adopted by BitTorrent [3] networks) into the unstructured file sharing game to model the competition in which a connection can be set up only when both users find this connection beneficial. We refer to this as an overlay formation game. We prove the existence of Nash equilibrium in several variants of both games, and quantify the losses of efficiency of Nash equilibria. We find that the loss of efficiency due to selfish behavior is still unbounded even when the Tit-for-Tat strategy is believed to prevent selfish behavior.