In this work, we consider the broadcast mechanisms for both reliable links and unreliable links in the Internet of Things (IoT) networks. Focusing on the minimum transmission broadcast (MTB) problem, we propose an efficient algorithm, termed as the Connected Dominating Set Algorithm based on Coalitional Graph Game (CDSA-CGG), to find the minimum connected dominating set (MCDS). Distinct from related work in the literature which adopts a non-cooperative game approach and assumes the interaction among nodes is limited to neighboring nodes, we formulate the interaction and cooperation among nodes over reliable links and over unreliable links as a connected forwarding graph based on coalitional graph game. We prove that the forwarding graph constructed by CDSA-CGG is a Nash network. In addition, we also prove that the final resulting graph is pairwise stable. The simulation results show that the proposed coalition graph game-based algorithm performs well in terms of the number of transmissions, convergence rate, and lifetime of nodes.