Maximal Covering Location Problem and Bimatrix Games

The problem of optimally locating service centers to maximize customer coverage within a specified distance remains both theoretically significant and practically relevant. This article presents a game-theoretic approach to solving such location-allocation problems, offering a comprehensive framework that identifies all viable facility configurations while evaluating their strategic stability. The methodology enables the discovery of alternative solutions that may be preferable under specific conditions, considering both maximum coverage objectives and system-wide stability requirements. The study examines the case of two service centers planned for organizational merger, with the approach being extensible to multiple facilities. The proposed technique provides new theoretical insights into location problems while offering practical applications across various domains. Potential implementations include retail network optimization during corporate consolidations, strategic placement of specialized healthcare facilities, and deployment of critical public infrastructure services. A regional case study illustrates how equilibrium-based solutions outperform traditional approaches by simultaneously maintaining service accessibility and ensuring long-term network stability.