Compartmental observability approach for the optimal transparency problem in multi-agent systems

This paper considers a network of agents, where each agent is assumed to take actions optimally with respect to a predefined payoff function involving the latest actions of the agent's neighbors. Neighborhood relationships stem from payoff functions rather than actual communication channels between the agents. A principal is tasked to optimize the network's performance by controlling the information available to each agent with regard to other agents’ latest actions. The information control by the principal is done via a compartmental observability approach, which comprises a static partitioning of agents into blocks and making the mean of agents’ latest actions within each block publicly available. While the problem setup is very general in terms of the payoff functions and the network's performance metric, the paper has a narrower, yet still fairly general, focus to display essential characteristics of the problem and to show how it can be addressed in practice. In particular, the performance metric is assumed to be a function of the steady-state behavior of the agents. After conducting a comprehensive steady-state analysis of the network, two efficient heuristic algorithms finding nearly-optimal partitions with respect to various performance metrics are presented and validated via numerical studies.