Several areas of wireless networking, such as wireless sensor networks or the Internet of Things, require application data to be distributed to multiple receivers in an area beyond the transmission range of a single node. This can be achieved by using the wireless medium’s broadcast property when retransmitting data. Due to the energy constraints of typical wireless devices, a broadcasting scheme that consumes as little energy as possible is highly desirable. In this article, we present a novel multi-hop data dissemination protocol called BTP. It uses a game-theoretical model to construct a spanning tree in a decentralized manner to minimize the total energy consumption of a network by minimizing the transmission power of each node. Although BTP is based on a game-theoretical model, it neither requires information exchange between distant nodes nor time synchronization during its operation, and it inhibits graph cycles effectively. The protocol is evaluated in Matlab and NS-3 simulations and through real-world implementation on a testbed of 75 Raspberry Pis. The evaluation conducted shows that our proposed protocol can achieve a total energy reduction of up to 90% compared to a simple broadcast protocol in real-world experiments.