In underwater acoustic sensor networks (UASNs), power allocation is a critical challenge owing to the need to balance energy efficiency and communication quality. To address this issue, we propose a distributed power control algorithm based on a Stackelberg game integrated with a pricing mechanism. The approach incorporates residual energy awareness at relay nodes and employs multivariate data analysis, including channel gain and transmission cost, to achieve an effective trade-off between energy efficiency and cooperative performance. The interaction between source and relay nodes is modeled as a hierarchical game in which the source node, acting as the leader, minimizes its transmission and relay payment costs, while the relay nodes, as followers, dynamically adjust their power pricing to maximize revenue and reduce energy consumption. Optimal response strategies are derived using Lagrangian multipliers, and the existence and uniqueness of the Nash equilibrium are established. To adapt to time-varying channel conditions, a distributed iterative algorithm that relies only on local information is developed, thereby reducing signaling overhead and overall system cost. Simulation results demonstrate that the proposed method significantly improves the network lifetime, enhances the average transmission rate, and increases the energy efficiency of the nodes.