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The resource-constrained nature of IoT objects makes the Routing Protocol for Low-power and Lossy Networks (RPL) vulnerable to several attacks. Although RPL specification provides encryption protection to control messages, RPL is still vulnerable to internal attackers and selfish behaviours. To address the lack of robust security mechanisms in RPL, we design a new Metric-based RPL Trustworthiness Scheme (MRTS) that introduces trust evaluation for secure routing topology construction. Extensive simulations show that MRTS is efficient in terms of packet delivery ratio, energy consumption, nodes’ rank changes, and throughput. In addition, a mathematical modelling analysis shows that MRTS meets the requirements of consistency, optimality, and loop-freeness and that the proposed trust-based routing metric has the isotonicity and monotonicity properties required for a routing protocol. By using game theory …