A group of agents able to generate consolidated income by specific private investments (efforts) is considered. A strictly convex function that increases as the value of the investment of each agent increases is used as the value of the expected consolidated income. The agents are familiar with the relation of the expected income to the size of investments. At the same time, each team member pursues only the individual interests and aims to maximize his/her own gain. It is assumed that there may be a small group of agents (coalition) within a team who enjoy a fairly high level of confidence in the other team members and have no other means of influencing their behavior. In order to maximize its own gain and based on its members’ chosen investment strategy, the coalition determines the distribution rule for the consolidated income for all the team members and gives them all the necessary information about this rule and the amounts of their own investments. Agents who are not members of the coalition and who consider this information reliable will accept the coalition’s proposal if the amount of the expected individual gain for each agent exceeds its expected value in an alternative option in the form of the Nash equilibrium. Conditions determining the size and structure of the coalition are found within the model, and when these conditions are met, the Stackelberg equilibrium is Pareto superior to the Nash equilibrium. Connections are made between the individual characteristics of the coalition members and the integral characteristics of every team member both with the coalition size and structure, as well as with the corresponding investment amounts and the values of consolidated and individual gains.