Aiming at the problems of UWSNs, such as unstable network topology control, unbalanced energy consumption caused by frequent changes and short network lifetime, this paper starts with the analysis of the evolution of topology caused by underwater uncertainties of sensor nodes, builds a state variable description model of distributed underwater sensor nodes, and concludes the multi-objective interaction and collaboration between nodes and environment. Topology control optimization problem for decision-making is mapped into game theory optimization problem. Then, potential game and Log-linear distributed learning rules are used to update the strategy behavior of nodes in the game. The non-homogeneous Markov chain theory is used to prove that the optimization problem of network topology control objective function converges to the solution of maximizing potential game function, so as to achieve guaranteeing. The purpose of maintaining network balance and prolonging network lifetime is to achieve the goal of maintaining network balance.