On one Saddle Point Search Algorithm for Continuous Linear Games as Applied to Information Security Problems

Authors: Bykov A.Yu., Krygin I.A., Grishunin M.V., Markova I.А. Published: 20.12.2020
Published in issue: #4(133)/2020  
DOI: 10.18698/0236-3933-2020-4-58-74

Category: Informatics, Computer Engineering and Control | Chapter: Methods and Systems of Information Protection, Information Security  
Keywords: information security, game theory, zero-sum game, continuous game, saddle point, linear programming

The paper introduces a game formulation of the problem of two players: the defender determines the security levels of objects, and the attacker determines the objects for attack. Each of them distributes his resources between the objects. The assessment of a possible damage to the defender serves as an indicator of quality. The problem of a continuous zero-sum game under constraints on the resources of the players is formulated so that each player must solve his own linear programming problem with a fixed solution of the other player. The purpose of this research was to develop an algorithm for finding a saddle point. The algorithm is approximate and based on reducing a continuous problem to discrete or matrix games of high dimension, since the optimal solutions are located at the vertices or on the faces of the simplices which determine the sets of players' admissible solutions, and the number of vertices or faces of the simplices is finite. In the proposed algorithm, the optimization problems of the players are sequentially solved with the accumulated averaged solution of the other player, in fact, the ideas of the Brown --- Robinson method are used. An example of solving the problem is also given. The paper studies the dependences of the number of algorithm steps on the relative error of the quality indicator and on the dimension of the problem, i.e., the number of protected objects, for a given relative error. The initial data are generated using pseudo-random number generators


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