Feedback Control in Multi-Agent Markovian networks*

In this paper, we consider a decision-making problem in a multi-agent setting, where each agent’s decisions can be influenced by others, and the corresponding decision-making process, also accounting for the external influences, is described by a Markovian model. The environment or a group of one or more agents may act then as a controller, that is, intending to steer the other agents toward a desired decision. In the considered setting, we formulate the problem of controlling the probability that a set of agents make a specific decision as a Model Predictive Control problem with equality constraints. The explicit solution to the MPC problem is derived as a set of state-feedback control laws. An illustrative example shows how the interaction between a broker and its clients can be modeled and marketing strategies decided as a solution to a constrained control problem.