In this paper, we apply the concepts of Markov decision evolutionary games to non-cooperative forwarding con- trol of Delay Tolerant Networks (DTN). Specifically, we rely on the design of mechanisms at the source node to study forwarding probability of the message in a DTN using the two- hop routing. We study the forwarding probability as a function of the competition within a large population of mobiles which need occasionally to make some action. In particular, for each message generated by a source, each mobile may take a decision that concerns the strategy by which the mobile participates to the relaying of the message from source to destination. A mobile that participates receives a unit of reward if it is the first to deliver a copy of the packet to the destination. The action taken by a mobile determine not only the immediate reward but also the transition probability to its next battery energy state. We characterize the Evolutionary Stable Strategies (ESS) for these games and propose a method to compute them. We also propose a mechanism design at the source in order to maximize the message delivery probability to the destination, given the equilibrium behavior (called Evolutionary Stable Strategy - ESS).