The paper applies an extended mean‑field game framework to model policyholder behavior in a large mutual insurance company, where surplus/deficit is shared among members. It proves global existence and uniqueness of the Nash equilibrium, characterized by constrained MF‑FBSDEs, and solves these numerically using a modified deep BSDE algorithm. Key findings include: insurance demand rises with risk aversion, loss volatility, and surplus‑sharing ratio; optimal coverage decreases toward the horizon; practical no‑short‑selling constraints reduce wealth disparities; and pool composition affects all members' strategies through interdependence. Extensions to survival models and decentralized insurance are proposed.