The computation problem of the optimal position of collaborating mobile robots equipped with omnidirectional cameras for visual area coverage is the subject of this paper. The planar area has several stationary obstacles resulting in a computationally intractable search scheme. Rather than using gradient-based search methods, the multi-agent swarm is clustered to partially deal with the dimensionality curse. Each cluster is end-to-end connected and its area of responsibility is assigned based on its collective Voronoi tessellation. This area is then coarsely sampled and a game-theoretic approach is employed relying on fictitious play amongst the cluster’s members. The search scheme is then switched into a fine-spatial sampling and initialized using the previously attained coarse optimal positions of the agents. The provided adaptive-size game-theoretic optimization search approach provides the optimal location of the agents with a tenfold faster convergence compared to the gradient-search methods. Simulation studies are offered to highlight the efficiency of the search scheme.