Influence Estimation of the Systemic Effect on Performance Antagonistic Games

Purpose of research. The estimation problem of the influence of the systemic effect on the performance of the antagonistic games of several participants, who play the game, acting in various ways, is considered. It is assumed, that players play games, match through independent, incompatible actions, or through concerted, joint actions.

Methods. It is obvious that joint actions provide greater efficiency, but such a qualitative estimation is often not enough. For informed decision making, as a rule, quantitative estimations are required.

Results. The analytical and computer solutions of the well-known equations describing the state of dynamic systems in which random Markov processes occur are used to obtain quantitative  estimates. The result of incompatible actions of the players is considered as the result of many independent events, while the process due to the combined actions of the players appears to be the result of the functioning of some dynamic system. The increase in the productivity of joint actions of players compared with incompatible actions is considered to be a consequence of the organization of several players as a dynamic system, and is called the system effect. Analytical solutions of the “dynamics  of  averages”  equations  obtained  earlier  by  Russian  and  foreign  mathematicians  are  used  for  a quantitative, approximate estimation of the influence of the systemic effect. The exact Kolmogorov equations describing changes in the probabilities of the state of dynamical systems with random processes were solved by computer methods using MATLAB.  These decisions made  it possible to obtain  estimates of the numerical values of the coefficient  of systemicity, which characterizes the effectiveness of joint actions compared to incompatible ones.

Conclusion. The results obtained in the article can be used to estimate the performance of the various training methods of participants in antagonistic games, athletes, and in educational institutions. 

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