Informational Design of Dynamic Multi-Agent System

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 (principal) 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 principal, such that the design process avoids the predictions of the agents' strategic selection behaviors. Based on the obedient principle, we introduce the design protocol given a goal of the principal referred to as obedient implementability (OIL) and study a Myersonian information design that characterizes the OIL in a class of obedient sequential Markov perfect Bayesian equilibria (O-SMPBE). A framework is proposed based on an approach which we refer to as the fixed-point alignment that incentivizes the agents to choose the signal sent by the principal, makes sure that the agents' policy profile of taking actions is the policy component of an O-SMPBE, and the principal's goal is achieved. 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.