Ignatenko O. Methods, models ant tools of mitigation malicious activity in open informational environments based on game theory.

This thesis deals with models, methods and tools of control of Open Informational Environments (OIE), providing services to users under conflict and uncertainty. For instance, Internet and multiprocessor computers are examples of OIE’s. In first case service is a bandwidth, in second – computation resources. It is proposed game theory approach to analysis of users competition over system resources, users interactions and malicious attacks, trying to disrupt system performance. In this work game-theory based model of controlled network with many selfish users was developed and conditions on Nash equilibrium existence and uniqueness are presented. Then model was extended to include real-world effects (queues, losses, window of TCP algorithm). Using differential equations with discontinuous right side it was proved existence and uniqueness of solution for model of TCP key feature (AIMD scheme). For game with N users it was formulated payoff matrix for a network game and found conditions of equilibrium existence depending of loss sensitivity parameter. For problem of scheduling and load balancing it was proposed model using a game-theoretic framework. The general objective was to identify and address the efficiency problems, where game theory can be applied to the model and evaluate user conflicts problems and consequently to design efficient solution. We consider the fluid model of computations to calculate the "ideal" complete time, which gives the lower bound of possible real time. We propose the game model of user's interaction on the example of matrix multiplication problem with centralized planner of extr-extr type. It was provided game theory analysis of planner and found the conditions of Nash equilibrium uniqueness, which is Pareto inefficient. Game theory provides mathematical base for analyzing and modeling security problems with many agents which could interact in complex, dynamic environment. The advantage of game theory approach is possibility of analyzing many different scenarios before adopting a certain strategy. Using mathematical modeling we provide simulations of network topology, controlling algorithms and users’ actions. Then we introduce network attacker into system and estimate attack influence on equilibrium characteristics. Using this approach we formulated theory-based estimations of network topology resilience and how attack will affect network equilibrium. Key words: denial of service attacks, game theory, Nash equlibria, conflict-controlled processes, grid, cloud computing, controlled multiprocessor computations, Internet protocols.