Approaches of probabilistic modeling to solving problems associated with incomplete information or fuzzy computations are the most common, but not the only ones. Among the important actual mathematical problems, the following tasks stand out: team selection and team composition, functions and roles distribution, team cohesion, performance level, transformational leadership. Mathematical models of team formation, as a rule, reflect the described properties of the teams: models of autonomous and joint activity, models of formal and informal teams, temporary and permanent teams, functional and creative teams. For example, models of synergistic effect in the theory of corporate games take into account emergence. Reputation models (Jean Tirole’s model or ShapiroStiglitzmodel) take into account stability, collaboration and unity of purpose. On the contrary, most models, like the well-known Holmstrom’s model, do not reflect such features as specialization and complimentarily of roles in the team, individual contribution to the overall result of the activity. Game theory describes a wide repertoire of agent strategies and includes reflexive games, evolutionary games and behavioral games. All of them are aimed at strategies of “decision-making” by agents (team members) in a statics or dynamics. Such models are widely used in economics, management and production. The interest of this study is assignment problem as classical match problem of team optimization, but in a neoclassical setting (not same for game theory). Universal parameters for modeling remain the same: team composition (multiplicity of agents); total performance (target function), functions and states of agents, team effectiveness. A new formulation of team formation problem is connected with the characteristics of collaboration: specialization (distribution and redistribution of roles), complementarities (interdependence), compatibility (individual and group) and participation. The search for the solution is aimed at calculating the optimal team composition with maximum of total performance and efficiency of teamwork (maximum result at minimum cost). This task is most relevant for sport games and requires a mathematical model for assessing the objective and subjective factors of dynamic interactions.