Incentive-compatible control in dynamic multi-agent systems. Part 1. Contracts in dynamic system with one principal and multiple agents

The formulation and solution are considered of the problems of coordinated control of multi-element dynamic active systems (AS) with restrictions on the joint activity of their elements in the form of technological networks. An AS is studied consisting of one principal and many agents subordinate to it. It has been proved that for any admissible trajectory of results, a coordinated compensatory incentive system can be constructed that implements (as an equilibrium in dominant strategies) the trajectory of the agents leading to the desired trajectory of results; decomposes the control task by agents and by time periods; provides guaranteed (for all possible far-sighted agents) minimum costs of the governing body of the principal for the implementation of this trajectory of results. It is shown that in such incentive systems, the values of payments depend only on the corresponding values of the cost functions, which, in turn, indirectly take into account the technological functions, network structure and AS structure as a whole. The problem of optimal planning is posed and an algorithm for solving it is indicated.