In this article, a new game theoretical method is proposed to model packet forwarding in relay networks. A simple case of relay network that consists of a source, a relay and a destination node communicating on a common channel is considered. A stationary Markovian game model is utilized to optimize the system performance in terms of throughput, delay and power consumption cost. Both cooperative and non-cooperative solutions are provided for this model. Best strategy set taken by players as well as system performance is studied for different system parameters. Also, the proposed method is extended to model a more general case of Ad-hoc networks considering different packet error rates in case of collision occurrence that improves the system performance further. Simulation results show that performance of the noncooperative solution, in which players do not require to know each other’s selected strategy, asymptotically approaches the cooperative system performance. Hence, the proposed model with non-cooperative solution is an appropriate method to apply in practical Ad-hoc networks.