Internet of things (IoT) is a very important research area, having many applications such as smart cities, intelligent transportation system, tracing, and smart homes. The underlying technology for IoT are wireless sensor networks (WSN). The selection of cluster head (CH) is significant as a part of the WSN's optimization in the context of energy consumption. In WSNs, the nodes operate on a very limited energy source, therefore, the routing protocols designed must meet the optimal utilization of energy consumption in such networks. Evolutionary games can be designed to meet this aspect by providing an adequately efficient CH selection mechanism. In such types of mechanisms, the network nodes are considered intelligent and independent to select their own strategies. However, the existing mechanisms do not consider a combination of many possible parameters associated with the smart nodes in WSNs, such as remaining energy, selfishness, hop-level, density, and degree of connectivity. In our work, we designed an evolutionary game-based approach for CH selection, combined with some vital parameters associated with sensor nodes and the entire networks. The nodes are assumed to be smart, therefore, the aspect of being selfish is also addressed in this work. The simulation results indicate that our work performs much better than typical evolutionary game-based approaches.