Delay tolerant networks (DTNs) rely on the mobility of nodes and sequences of their contacts to compensate for lack of continuous connectivity and thus enable messages to be delivered from end to end in a "store-carry- forward" way. Since each node may also need to deliver out its locally generated message, in addition to carrying and forwarding messages for other nodes, the node may become more willing to forward its own message rather than that of others when it encounters some node. This kind of selfish behaviors may become much more significant when the nodes are operating under both QoS requirements (e.g., delivery delay requirements) and energy constraints. In this paper, we analytically explore how this kind of selfish behaviors will influence the delivery performance of the two-hop relay in the challenging DTNs. In particular, a continuous time Markov chain-based theoretical framework is developed to model the complicated message delivery process. With the help of the theoretical framework, closed-form expressions are further derived for both the expected delivery delay and the expected delivery cost, where the important node selfishness issue is carefully incorporated into the analysis.