In this letter, we investigate user-centric access point (AP) selection for cell-free massive multiple-input multiple-output (MIMO) systems. In contrast to existing works, we study this problem from the perspective of game theory and model user-centric AP service cluster formation as a local altruistic game, which is proven to be an exact potential game (EPG) and to have at least one pure Nash equilibrium (NE). Then, an improved maximum non-neighbor-set-based concurrent spatial adaptive play (MNSB-C-SAP) algorithm is proposed to achieve the NE. Simulation results show that the proposed algorithm outperforms existing algorithms in terms of convergence speed and verify the superiority of the game-theoretic AP selection method compared with some existing approaches.