We consider the capacity problem (or, the single slot scheduling problem) in wireless networks. Our goal is to maximize the number of successful connections in arbitrary wireless networks where a transmission is successful only if the signal-to-interference-plus-noise ratio at the receiver is greater than some threshold. We study a game theoretic approach towards capacity maximization introduced by Andrews and Dinitz (INFOCOM 2009) and Dinitz (INFOCOM 2010). We prove vastly improved bounds for the game theoretic algorithm. In doing so, we achieve the first distributed constant factor approximation algorithm for capacity maximization for the uniform power assignment. When compared to the optimum where links may use an arbitrary power assignment, we prove a $O(\log Δ)$ approximation, where $Δ$ is the ratio between the largest and the smallest link in the network. This is an exponential improvement of the approximation factor compared to existing results for distributed algorithms. All our results work for links located in any metric space. In addition, we provide simulation studies clarifying the picture on distributed algorithms for capacity maximization.