In this paper, we apply evolutionary games to non-cooperative forwarding control in Delay Tolerant Networks (DTNs). The main focus is on mechanisms to rule the participation of the relays to the delivery of messages in DTNs. Thus, we express the success probability as a function of the competition that takes place within a large population of mobiles, and we characterize the effect of reward-based mechanisms on the performance of such systems. Devices acting as active relays, in fact, sacrifice part of their batteries in order to support message replication and thus increase the probability to reach the destination. In our scheme, a relay can choose the strategy by which they participate to the message relaying. A mobile that participates receives a unit of reward based on the reward mechanism selected by the network. A utility function is introduced as the difference between the expected reward and the energy cost, i.e., the cost spent by the relay to sustain forwarding operations. We show how the evolution dynamics and the equilibrium behavior (called Evolutionary Stable Strategy – ESS) are influenced by the characteristics of inter contact time, energy expenditure and pricing characteristics. We extend our analysis to mechanisms that the system can introduce in order to have the message delivered to the destination with high probability within a given deadline and under energy constraints which bound the number of released copies per message. Finally, we apply our findings in order to devise decentralized forwarding algorithms that are rooted in the theory of stochastic approximations. Thus, we demonstrate that the ESS can be attained without complete knowledge of the system state and letting the source monitor number of released copies per message only. We provide extensive numerical results to validate the proposed scheme.