Opinion Dynamic Games Under One Step Ahead Optimal Control

Abstract

This article generalizes two recently proposed opinion dynamics models with control. The generalized model consists of a standard model of agents interacting with each other, to which affine control inputs from players are added. The controls, influencing the opinions of agents, are exercised by entities called players, who specify targets, possibly conflicting, for agents. Three game-playing procedures are defined: sequential, parallel, and asynchronous. Each player has knowledge of the current state of all agents, but no other information about the other players. The player controls are designed using one step ahead optimization. This leads to several novel results: easily computable control policies for each player that depend only on the player's own information and conditions for convergence to the equilibrium as well as formulas for the latter. Comparisons showing advantages over prior Riccati equation-based methods for networks of different sizes are provided. The code to reproduce all examples and simulations is available on the GitHub site. Overall, the main contribution is the one step ahead optimal control (OSAOC) framework for influencing multiagent opinion dynamics in a decentralized game-theoretic setting.