To the theory of collective actions. Part 4. Use of violence potential

The subject of this research is opportunities for effective use of human capital members of the collective in the conditions of 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. Achievement of the socially optimal level of applied efforts requires coordination of actions based on the high level of trust between all members of the collective. Within the framework of mathematical model, it is demonstrated that the lack of trust to some extent can be compensated by the incentives based on the use of violence potential. Most successful implementation of such type of incentives is possible only in the relatively small collectives in the conditions of inevitability of punishment for violation, and cautions use of force. In large collectives, a low probability of punishment for violence turns out either in low significance of the expected punishment, or extremely high meaning of nominal punishment. In first instance, a threat of punishment can play a role of a constraining factor; while on the other instances – lead to a stiff punishment that may reduce the usefulness of a violator to an extremely low level. Therefore, the achieved by the collective result can be incomparable by Pareto even with Nash equilibrium.