Analysis of Equilibria in Systems with Endogenously Formed Utility Functions

A direct mechanism of impact on the utility functions of agents in social and economic systems is studied. This mechanism is widely used in various forms by public authorities, commercial and non-profit organizations for reaching the desired behavior of individuals. A game-theoretic model of a hierarchical system composed of agents and super-individuals who can modify their utility functions is considered. The properties of equilibria in this model are investigated and the systems of different structure are compared with each other in terms of efficiency. It is established that the centralized management of super-individuals in certain conditions may be less effective in terms of maximizing public welfare than the decentralized schemes. In particular, this property can explain the successful development of peer-to-peer markets and decentralized financing mechanisms of projects in various spheres of human activity. Also, the presence of vertical competition effects in the system is demonstrated, which reduce the efficiency of equilibria with increasing the number of super-individuals.