IoT objects that have a resource constrained nature resulting in a number of attacks in the routing protocol for lossy networks and low-power networks. RPL is very vulnerable to selfish behaviours and internal attacks though they are built with encryption protection to secure messages. To address this vulnerability, in this paper, we propose a novel trustworthiness methodology based on metric for incorporating trust evaluation, enhancing the robustness of security mechanism. Simulation results indicate that the proposed work is efficient in terms of throughput, nodes' rank changes, energy consumption and packet delivery ratio. Moreover, using mathematical modelling, it has been observed that this methodology meets the demands of loop-freeness, optimality and consistency. This shows that this metic has both monotonicity and isotonicity requirements to enable the routing protocol. Incorporating the concepts of game theory, we can use this technique as a strategy to iterate Prisoner's Dilemma. Both evolutionary simulation and mathematical analysis indicate that the proposed metric-based routing protocol is an efficient technique in promoting evolution and stability of the IoT network.