In wireless sensor networks (WSNs), the presence of congestion increases the ratio of packet loss and energy consumption and reduces the network throughput. Particularly, this situation will be more complex in Internet of Things (IoT) environment, which is composed of thousands of heterogeneous nodes. RPL is an IPv6 routing protocol in low power and lossy networks standardized by IETF. However, the RPL can induce problems under network congestion, such as frequently parent changing and throughput degradation. In this paper, we address the congestion problem between parent nodes and child nodes in RPL-enabled networks, which typically consist of low power and resource constraint devices. To mitigate the effect of network congestion, we design a parent-change procedure by game theory strategy, by which the child nodes can change next hop neighbors toward the sink. Comparing to the ContikiRPL implementation, the simulation results show that our protocol can achieve more than two times improvement in throughput and reduce packet loss rate with less increasing of average hop count.