The application of unmanned ae-rial vehicle (UAV)-mounted base stations is emerging as an effective solution to provide wireless communication service for a target region containing some smart objects (SOs) in intet of things (IoT). This paper inves-tigates the efficient deployment problem of multiple UAVs for IoT communication in dy-namic environment. We first define a measure-ment of communication performance of UAV-to-SO in the target region which is regarded as the optimization objective. The state of one SO is active when it needs to transmit or receive the data; otherwise, silent. The switch of two different states is implemented with a certain probability that results in a dynamic communication environment. In the dynamic environment, the active states of SOs can-not be known by UAVs in advance and only neighbouring UAVs can communicate with each other. To overcome these challenges in the deployment, we leverage a game-theoretic leing approach to solve the position-se-lected problem. This problem is modeled a stochastic game, which is proven that it is an exact potential game and exists the best Nash equilibria (NE). Furthermore, a distributed position optimization algorithm is proposed,which can converge to a pure-strategy NE. Numerical results demonstrate the excellent performance of our proposed algorithm.