DEVELOPMENT OF A MODEL FOR DECISION SUPPORT SYSTEMS FOR MANAGING THE PROCESS OF INVESTING IN CYBERSECURITY TAKING INTO ACCOUNT MULTIFACTORIALITY

A model for managing the investment process is proposed, based on the example of investing in cybersecurity of national scale informatization objects, taking into account the multifactorial nature of this process. The difference between this model and those previously developed is that, firstly, it considers the investment process as a complex structure, for which it is not enough to model it as a one-factor category. Second, our model is based on the solution of a bilinear multi-step quality game with several terminal surfaces. The solution is obtained within the framework of the scheme of a new class of bilinear multistage games describing the interaction of objects in a multidimensional space. Consideration of the investment process in such a setting makes it possible to adequately describe the process of searching for rational strategies of players in the course of investing in information technologies. The study made it possible to implement the program code of the model in the MatLab simulation environment.

The Revelation Principle in Multistage Games

The communication revelation principle (RP) of mechanism design states that any outcome that can be implemented using any communication system can also be implemented by an incentive-compatible direct mechanism. In multistage games, we show that in general the communication RP fails for the solution concept of sequential equilibrium (SE). However, it holds in important classes of games, including single-agent games, games with pure adverse selection, games with pure moral hazard, and a class of social learning games. For general multistage games, we establish that an outcome is implementable in SE if and only if it is implementable in a canonical Nash equilibrium in which players never take codominated actions. We also prove that the communication RP holds for the more permissive solution concept of conditional probability perfect Bayesian equilibrium.

Strong Strategic Support of Cooperation in Multistage Games

The problem of cooperation in repeated and multistage games is considered. The strong equilibrium (equilibrium stable against deviations of coalitions) with payoffs which can be attained under cooperation is constructed for a wide class of such games. The new solution concept based on solutions of stage games is introduced and in some cases this solution is a subset of the core defined for repeated and multistage games in a classical way. It is also proved that this newly introduced solution concept is strongly time consistent. The strong time consistency of the solution is a very important property since in case it does not take place players in reality in some time instant in subgame on cooperative trajectory may switch from the previously selected optimal solution to any other optimal solution in the subgame and as result realize the solution which will not be optimal in the whole game.

A Note on Strategic Stability of Cooperative Solutions for Multistage Games

The problem of strategic stability of cooperative solutions for multistage games is studied. The sufficient conditions related to discount factors are presented, which guarantee the existence of Nash or strong Nash equilibria in such games and therefore guarantee the strategic stability of cooperative solutions. The deviating payoffs of players are given directly, which are related closely to these conditions and avoid the loss of super-additivity of a class of general characteristic functions. As an illustration, Nash and strong Nash equilibria are found for the repeated infinite stage Prisoner’s dilemma game.