A dynamic cooperative games formalization of the problem of concordance of interests of the social partnership agents the the system of continuing professional education is proposed. The setup based on the previously considered differential games in normal form. The time consistency problem and its sociological interpretation are discussed.

Keywords: differential games in normal form, differential cooperative games, time consistency, continuing professional education, social partnership

A game-theoretic dynamic model of social partnership in the system of continuing professional education is proposed and investigated in the simulation mode on the base of scenario method. The processing of modeling data includes a comparative analysis of state variable and payoff functionals. Results of the model identification and investigation based on simulation modeling are considered. A comparative analysis of egoistic and cooperative approaches to the social partnership is conducted.

Keywords: social partnership, continuing professional education, simulation modeling, identification, difference games

A cooperative game theoretic model of dynamics of the trust level between subjects of the system of optional professional education is proposed. Some approaches to the model identification and investigation based on simulation modeling and differential cooperative game theory are considered.

Keywords: social partnership, optional professional education, differential cooperative games, simulation modeling, identification

Relations between subjects of the system of social partnership in the domain of optional professional education are modeled by a voting game. For the 3-person voting game a comparative analysis of such optimality principles as C-core, NM-decision, and Shapley value for the typical values of the players' voices is conducted.

Keywords: social partnership, optional professional education, voting games, C-core, NM-decision, Shapley value

The mathematical model formalizes the solution of a problem of optimum control and it is meaningful to minimization of number of regional extremist system (bandit underground) taking into account relative importance of parts making it at the restrictions caused by "will" of the state to fight against extremism and objective dynamics of number of groups of extremists, an ethnosociocultural protestnost defined by factors (protest potential of society). The task was solved by means of imitating modeling on a method of scenarios.

Keywords: Mathematical model, method of scenarios, extremism, dynamics of number of groups of extremists, problem region, North Caucasus.

The mathematical model formalizes the solution of a problem of optimum control and  the minimization of regional extremist system’s number (bandit underground) is meaningful taking into account the relative importance of its parts with the restrictions caused by "will" of the state to fight against extremism and the objective dynamics of the extremist groups number, defined by the ethno-and-sociocultural protest potential factors. The problem was solved by means of imitating modeling basing on scenarios method. The results of scenery modeling of republican bandit underground dynamics are obtained depending on different variants of the power influence, in conjunction with different options of republican community development. The results of modeling calculations on fixing of a range of scenarios of quantitative dynamics of separate groups layers of a republican bandit underground are given. The identification of modeling parameters according to scenarios is executed and interpretation of the received results and practical recommendations on optimization of combating regional terrorist underground is presented.

Keywords: Mathematical model, scenery modeling, extremism, bandit underground, dynamics of number of groups layers of extremists, problem region, North Caucasus.