The design of energy-efficient mechanisms is one of the key challenges in emerging wireless small cell networks. In this paper, a novel approach for opportunistically switching ON/OFF base stations to improve the energy efficiency in wireless small cell networks is proposed. The proposed approach enables the small cell base stations to optimize their downlink performance while balancing the load among each another, while satisfying their users' quality-of-service requirements. The problem is formulated as a noncooperative game among the base stations that seek to minimize a cost function which captures the tradeoff between energy expenditure and load. To solve this game, a distributed learning algorithm is proposed using which the base stations autonomously choose their optimal transmission strategies. Simulation results show that the proposed approach yields significant performance gains in terms of reduced energy expenditures up to 23% and reduced load up to 40% compared to conventional approaches.