A mathematical model for optimizing security measures for facilities based on matrix games

The relevance of this study stems from the need to formalize the antagonistic confrontation between facility security measures and the operational vulnerabilities of systems while simultaneously accounting for uncertainty and resource limitations. Therefore, this article aims to develop a mathematical model that enables the rational selection of the optimal composition of protective measures in conflict situations. The leading approach to studying this problem is the framework of matrix games, which allows for a comprehensive consideration of the interaction of protective strategies and destructive factors based on uniform expert criteria. The article presents three options for forming a payoff matrix (homogeneous and heterogeneous strategies, direct expert assessment of mutual influence), reveals mechanisms for finding a solution in pure strategies through a saddle point, identifies conditions under which a solution exists only in mixed strategies, and substantiates a method for calculating the proportions of combining heterogeneous protective measures to achieve a guaranteed result. The article's materials are of practical value to specialists designing physical and information security systems, as well as to decision makers who allocate limited resources to protected facilities under deliberate countermeasures.

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