Most research in human activity recognition is supervised, while non-supervised approaches are not completely unsupervised. In this paper, we provide a novel flexible multi-objective particle swarm optimization (PSO) clustering method based on game theory (FMOPG) to discover human activities fully unsupervised. Unlike conventional clustering methods that estimate the number of clusters and are very time-consuming and inaccurate, an incremental technique is introduced which makes the proposed method flexible in dealing with the number of clusters. Using this technique, clusters that have a better connectedness and good separation from other clusters are gradually selected. To improve the convergence speed of PSO in achieving the best solution and dealing with spherical shape clusters, updating of particles' velocity is modified using the concept of mean-shift vector. To solve multi-objective optimization problems, Nash equilibrium in game theory is used to select the optimal solution on the pareto front. Gaussian mutation is also employed on the pareto front to generate diverse solutions and create a balance between exploitation and exploration. The proposed method is compared with state-of-the-art methods on five challenging datasets. FMOPG has improved clustering accuracy by 3.65% compared to automated methods. Moreover, the incremental technique has improved the clustering time by 71.18%.