We consider a two-hop routing delay-tolerant network. When the source encounters a mobile then it transmits, with some probability, a file to that mobile, with the probability itself being a decision variable. The number of mobiles is not fixed, with new mobiles arriving at some constant rate. The file corresponds to some software that is needed for offering some service to some clients, which themselves may be mobile or fixed. We assume that mobiles have finite life time due to limited energy, but that the rate at which they die is unknown. We use an H∞ approach which transforms the problem into a worst case analysis, where the objective is to find a policy for the transmitter which guarantees the best performance under worst case conditions of the unknown rate. This problem is formulated as a zero-sum differential game, for which we obtain the value as well as the saddle-point policies for both players.