We analyse the performance of an incentive scheme for two-hop DTNs in which a back-logged source proposes a fixed reward to the relays to deliver a message. Only one message at a time is proposed by source. For a given message, only the first relay to deliver this message gets the reward corresponding to this message thereby inducing a competition between the relays. The relays seek to maximize the expected reward for each message whereas the objective of the source is to satisfy a given constraint on the probability of message delivery. We show that the optimal policy of a relay is of threshold type: it accepts a message until a first threshold and then keeps the message until it either meets the destination or reaches the second threshold. Formulas for computing the thresholds as well as probability of message delivery are derived for a backlogged source.