In this paper, problem of throughput optimization in relay networks where all users transmit their packets on a multiple-access channel is studied by introducing a new Markovian game theoretical solution. Despite the previously reported works, in the proposed model, simultaneously transmitted packets on a multiple-access channel are not always discarded. In this article, the possibility of capturing one of these packets is considered. Both cases of cooperative and non-cooperative stochastic game solutions are investigated and compared. The main objective is to maximize the system throughput with minimum transmission delay and power consumption cost. Effect of different packet error rates due to possible collision occurrence is considered in the game definition that improves system performance further. Performance of the proposed non-cooperative game model approaches the cooperative case, however the non-cooperative game model adds less signaling load to the system, therefore it is more likely to be used in practical applications.