Smart interference management methods are required to enhance the throughput, coverage, and energy efficiency of a dense small cell network. In this paper, we propose a transmit power control for energy efficient operation of a dense small cell network. We cast the power control problem as a noncooperative game to satisfy the design requirement that small cells do not need any information exchange among them. We analyze the sufficient condition for the existence of a Nash equilibrium (NE) state of the proposed game. We also analyze that the NE state is unique by transforming the original nonlinear fractional programming problem into a nonlinear parametric programming problem. Through simulation studies, we verify our analysis results. In addition, we show that the proposed method achieves higher energy efficiency of a network and balances the energy efficiency among cells more evenly than the methods based on the AIMD (additive increase and multiplicative decrease) algorithm.