This paper develops a multi-level game-theoretic framework for determining a cost-effective defensive strategy for protecting power systems from false data injection attacks like load redistribution attacks. First, a multi-level optimization problem considering interactions among defenders, attackers and operators is modeled based on the minimax-regret decision rule, which is then reformulated as an equivalent bi-level mixed-integer linear programming problem. Next, an implicit enumeration algorithm is developed to find a globally optimal solution to this complex bi-level problem. Several acceleration techniques are introduced to improve the computation efficiency of the proposed method for large-scale power system applications. Last, the proposed defensive strategy is validated by case studies based on a six-bus test system and a modified two-area RTS-96 system.