Opinion Dynamic Games under One Step Ahead Optimal Control

This paper generalizes two recently proposed opinion dynamics models with control. The generalized model is made up of a standard model of agents interacting with each other, to which affine controls are added. The controls, influencing opinions of agents, are exercised by entities called players, who specify targets, possibly conflicting, for agents. Three play procedures, sequential, parallel and asynchronous are defined. Each player has knowledge of the current state of all agents, but \textit{no other information about the other players}. We design the player controls using one step ahead optimization leading to the following novel results: easily computable controls for each player only dependent on its own information; conditions for convergence to the Nash equilibrium, and formulas for the latter.