Opinion dynamics of stubborn agents under the presence of a troll as differential game

The question of whether opinions of stubborn agents result in Nash equilibrium under the presence of troll is investigated in this study. The opinion dynamics is modelled as a differential game played by n agents during a finite time horizon. Two types of agents, ordinary agents and troll, are considered in this game. Troll is treated as a malicious stubborn content maker who disagrees with every other agent. On the other hand, ordinary agents maintain cooperative communication with other ordinary agents and they disagree with the troll. Under this scenario, explicit expressions of opinion trajectories are obtained by applying Pontryagin’s principle on the cost function. This approach provides insight into the social networks that comprise a troll in addition to ordinary agents