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The question of whether opinions of stubborn agents result in Nash equilibrium under the presence of troll 4 is investigated in this study. The opinion dynamics is modelled as a differential game played by n agents during a finite 5 time horizon. Two types of agents, ordinary agents and troll, are considered in this game. Troll is treated as a malicious 6 stubborn content maker who disagrees with every other agent. On the other hand, ordinary agents maintain cooperative 7 communication with other ordinary agents and they disagree with the troll. Under this scenario, explicit expressions of 8 opinion trajectories are obtained by applying Pontryagin’s principle on the cost function. This approach provides insight 9 into the social networks that comprises a troll in addition to ordinary agents. 10

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