Mathematical modeling of group concurrency in game theory

The approach to an estimation of results of group «competitions» of intellectual agents is described. Petri–Markov models group «competition» are analyzed. Expressions for the determination of the probability density distribution and the participants or groups of participants win or lose «competition» are given. In general, the temporal and probabilistic characteristics of the game are obtained. The technique for an estimation of sequence of victories in «competition» of groups of subjects is offered, the estimation of efficiency of «competitions» of groups is resulted. Are considered two most often used principle of distribution of penalties: the lost group pays the penalty to the won group; each participant of the lost group pays the penalty to the won group, and sizes of penalties are distributed on time.