Robots operating in multi-player settings must simultaneously model the environment and the behavior of human or robotic agents who share that environment. This modeling is often approached using Simultaneous Localization and Mapping (SLAM); however, SLAM algorithms usually neglect multi-player interactions. In contrast, the motion planning literature often uses dynamic game theory to explicitly model noncooperative interactions of multiple agents in a known environment with perfect localization. Here, we present GTP-SLAM, a novel, iterative best response-based SLAM algorithm that accurately performs state localization and map reconstruction, while using game theoretic priors to capture the inherent non-cooperative interactions among multiple agents in an uncharted scene. By formulating the underlying SLAM problem as a potential game, we inherit a strong convergence guarantee. Empirical results indicate that, when deployed in a realistic traffic simulation, our approach performs localization and mapping more accurately than a standard bundle adjustment algorithm across a wide range of noise levels.