Real-world interactions, such as web system access, tournaments, social communication, etc. can be modeled as a game with binary outcomes. Previous works study extracting the game’s underlying structure into a coordinate system with the most prominent pairwise Pareto non-dominated strategies, i.e. the discovery of underlying game objectives. Objective search has also been considered in a coevolutionary context. Our work, however, targets a scenario when mutual adjustment cannot occur. While the first player performs moves by nature, the second learns the underlying objectives. Inference of the black-boxed game structure occurs during the simulation. In this regard, we propose the coordinate system extraction (CSE) algorithm, capable of working with sparse interactions. Additionally, we consider a benchmark to probe the search algorithm’s robustness on predefined game coordinate system shapes. We compare approaches from coevolution such as parallel hill climbing and Pareto layering to a proposed CSE method on the benchmark, and conclude that CSE infers the underlying coordinate system better in terms of both performance and robustness.