We consider an opportunistic wireless communication setting, in which two nodes (referred to as forwarders) compete to choose a relay node from a set of relays, as they ephemerally become available (e.g., wake up from a sleep state). Each relay, when it becomes available (or arrives), offers a (possibly different) " reward " to each forwarder. Each forwarder's objective is to minimize a combination of the delay incurred in choosing a relay and the reward offered by the chosen relay. As an example, we develop the reward structure for the specific problem of geographical forwarding over a common set of sleep-wake cycling relays. In general, our model can be considered as a game theoretic variant of the asset selling problem studied in the operations research literature. We study two variants of the generic relay selection problem, namely, the completely observable (CO) and the partially observable (PO) cases. These cases are based on whether a forwarder (in addition to observing its reward) can also observe the reward offered to the other forwarder. Formulating both problems as a two person stochastic game, we characterize the solutions in terms of Nash Equilibrium Policy Pairs (NEPPs). For the CO case we provide a general structure of the NEPPs. For the PO case we prove that there exists an NEPP within the class of threshold policy pairs. Through numerical work, for a one-hop forwarding example we compare the cost performance of various NEPPs with a simple forwarding (SF) policy which causes each forwarder to act as if the other is not present. We find that if the forwarders are not very close then the SF policy suffices. Insights gained from this numerical work are then used in an end-to-end simulation of geographical forwarding in a large network, in which we are concerned with delivery of packets from a tagged source to a sink, in the presence of competition from other packet flows destined to the same sink.