The era of single processors had almost reached a saturation state, and the industry had moved to multi-core processors for the newer generation of many-core architecture. Interconnections between multiple cores with network on chip (NoC) surpass traditional bus architecture for its quality of service (QoS) and other additional services. Seamless communication among the cores is more significant for better performance and the proper utilization of the cores. The rise in the cores count in a semiconductor chip adds the complexity of the communication among cores. Cache misses request and packet transmission’s traffic possibly will reduce the performance of the architecture. A theoretical game-based methodology is proposed to improvise the performance and communication by routing the request packets in the NoC of the many core architectures and the throughput is maximized with reduced latency by using the stag-hunt game (SHG) model. The proposed communication algorithm routes the packets in an adaptive way by detecting the congestion in routers. The SHG based odd-even routing algorithm is adaptive and can divert the packets towards less congested routers using the information gathered about congestion in the system, so that the overall performance of the system in terms of latency and throughput is improved.