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This paper presents a two-stage opinion dynamics game model to investigate how two players influence an agent’s opinion within a Stackelberg game framework. Optimal control strategies are obtained via the Hamilton–Jacobi–Bellman equation. In the first stage, player 1, acting as the leader, exerts significant influence on the agent’s initial opinion trajectory through optimal control. In the second stage, player 2, as the follower, can partially guide the opinion, but the agent’s final opinion remains closer to player 1’s target due to the first-mover advantage. Theoretical results are supported by numerical simulations, highlighting the phased nature of the opinion trajectory and its dynamic relation to the players’ targets.

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Two-Stage Game Model of Opinion Dynamics

  • 会议论文

  • 发表日期：

    2025年

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  • Yanshan Liu,
  • Vladimir V. Mazalov,
  • Hongwei Gao

摘要

This paper presents a two-stage opinion dynamics game model to investigate how two players influence an agent’s opinion within a Stackelberg game framework. Optimal control strategies are obtained via the Hamilton–Jacobi–Bellman equation. In the first stage, player 1, acting as the leader, exerts significant influence on the agent’s initial opinion trajectory through optimal control. In the second stage, player 2, as the follower, can partially guide the opinion, but the agent’s final opinion remains closer to player 1’s target due to the first-mover advantage. Theoretical results are supported by numerical simulations, highlighting the phased nature of the opinion trajectory and its dynamic relation to the players’ targets.