Abstract
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.