Alexander G. Chkhartishvili

Dynamic models of informational control in social networks

The dynamic models of informational control in social networks were considered. The problems of analysis and design of the optimal controls were posed and examined.

Informational influence and informational control models in social networks

We model the forming and dynamics of opinions in a social network with Markov chains. We set and solve, for a number of special cases, the problems of controlling agent opinions and game-theoretic problems of informational conflict.

Reflexive games: Transformation of awareness structure

A game-based model of reflexive decision-making is proposed. Reflexive normal form game being repeated several times, some of the agents (or even all of them) are demonstrated to observe unexpected results of the game (e.g., actions of the opponents, values of payoff functions, etc); thus, awareness structure is modifled. We discuss three problems, notably, awareness structure, actions of the agents based on the structure, transformation of awareness structure.

Structural modeling of oligopoly market under the nonlinear functions of demand and agents' costs

In this paper, we consider the structural modeling problem of an oligopoly market for an arbitrary number of agents, the linear and nonlinear models of market demand, and the nonlinear models of agents’ costs. The equilibrium behavior of the agents is described on the basis of conjectural variations in the Cournot or Stackelberg reaction models (in the cases of one or several leaders). The adequacy of the Cournot reaction model is demonstrated using the equilibrium modeling of the Volga region telecommunication market, where the price functions and agents’ cost functions for the voice and Internet services are defined by statistical analysis methods.

A conceptual approach to online social networks analysis

This paper introduces a constructive approach to online social networks analysis. We suggest a conceptual model of a social network, formulate major problems of analysis and control in social networks, describe methods and algorithms for activity analysis in social networks, as well as technologies for social networks monitoring and analysis.

Game-theoretic models of an oligopoly market with nonlinear agent cost functions

We construct oligopoly models for nonlinear cost functions of agents under reflexive information. We obtain conditions for Nash equilibria under symmetric and asymmetric agent information in Cournot and Stackelberg reaction models (in case of one or several leaders).

An actional model of user influence levels in a social network

This paper suggests a new approach to the constructive definition of user influence levels in social networks—the so-called actional model. According to the approach, the influence level of a user is calculated on the basis of their actions taking into account the goals of a control subject (a Principal). An example illustrates how the actional model can be applied to find the influence level of users in a real social network on the assumption of available initial data.

A model of informational control in active network structures in case of an incomplete awareness of the principal

A model of informational control in network structures is analyzed. The result of informational control depends on the principal’s awareness and the influence levels of network structure elements (agents). Finally, the issue of beneficial network structures (from the principal’s viewpoint) is studied.

Concordant informational control

We propose a model of concordant informational control, where agents are informed about the fact of control implementation by a principal. Still, the agents trust messages of the principal. The existence conditions are established for such control and several properties are demonstrated.

Reflexion in mathematical models of decision-making

Abstract The paper is devoted to a generalization of static and dynamic mathematical models of behavior with explicitly stated reflexive models of agents’ decision-making. Reflexion is considered as agent’s beliefs about nature, opponents’ beliefs and opponents’ decision-making principles in the framework of game theory, collective behavior theory and learning models.