  This work considers a novel information design problem and studies how the
craft of payoff-relevant environmental signals solely can influence the
behaviors of intelligent agents. The agents' strategic interactions are
captured by an incomplete-information Markov game, in which each agent first
selects one environmental signal from multiple signal sources as additional
payoff-relevant information and then takes an action. There is a rational
information designer (designer) who possesses one signal source and aims to
control the equilibrium behaviors of the agents by designing the information
structure of her signals sent to the agents. An obedient principle is
established which states that it is without loss of generality to focus on the
direct information design when the information design incentivizes each agent
to select the signal sent by the designer, such that the design process avoids
the predictions of the agents' strategic selection behaviors. We then introduce
the design protocol given a goal of the designer referred to as obedient
implementability (OIL) and characterize the OIL in a class of obedient perfect
Bayesian Markov Nash equilibria (O-PBME). A new framework for information
design is proposed based on an approach of maximizing the optimal slack
variables. Finally, we formulate the designer's goal selection problem and
characterize it in terms of information design by establishing a relationship
between the O-PBME and the Bayesian Markov correlated equilibria, in which we
build upon the revelation principle in classic information design in economics.
The proposed approach can be applied to elicit desired behaviors of multi-agent
systems in competing as well as cooperating settings and be extended to
heterogeneous stochastic games in the complete- and the incomplete-information
environments.
