In this paper we study a simple relay channel where a transmitter can transmit a packet directly to the receiver or transmit through the relay. In such a case, there is an inherent trade-off between energy and delay since transmitting a packet directly to the receiver may consume more energy than transmitting through a relay whereas transmission through relay incurs more delay. We consider two cases; when nodes are cooperative and when nodes are strategic. We show that when nodes are strategic, there exist payment transfer functions to be exchanged between the nodes such that the socially optimal Markov policy is the unique sub game perfect equilibrium of the resulting dynamic game.
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