To the theory of collective actions. Part 2. Mathematical model

The subject of this research is the barriers that must be overcome by a collective of individual for the effective use of their self-governance and self-organization resources. It is assumed that members of the collective are capable to jointly create an additional cost by making individual efforts. Value of the expected gross income increases with the efforts put by each agent, and subordinated to the law of diminishing returns. The goal of each member of the collective consists in maximization of the own individual profit. Within the framework of mathematical modeling, it is demonstrated that in the regime of independent choice of the volume of applied effort, the agents achieve outcome that is the equilibrium by Nash, but inefficient by Pareto. Each member of the collective due to their egoistic intentions is interested in applying the limited amount of efforts that meet the maximum of his individual profit, but all his partners should apply as much efforts as possible. Overcoming of ineffective equilibrium requires coordination of efforts invested by all members of the collective. As follows from the model, the main obstacles on the way to effective usage of human resources by a collective in the regime of self-organization and self-governance is a post-contractual opportunism in form of shirking. The free-rider problem and motivation to opportunistic behavior are generated by the desire of each member of the collective to maximization of their own individual profit in the conditions of force of the law of diminishing returns.