基于局部优化规则的意见动力学泛化
Generalized Opinion Dynamics from Local Optimization Rules
AI总结：
本文研究了Hegselmann-Krause模型的泛化形式，探讨了影响强度与意见距离相关的条件，分析了均衡特性及外部力量对用户更新的影响。
摘要：
我们研究了Hegselmann-Krause（HK）模型在意见动力学中的泛化形式，纳入了观察到的社会系统中自然存在的特征和参数。第一个泛化是影响强度取决于代理意见距离的情况。在此设定下，我们确定了意见在有限时间内收敛的条件，并提供了均衡的定性描述。我们将HK模型的意见更新规则解释为二次成本最小化规则。这使得第二个泛化成为可能：一系列具有不同均衡特性的更新规则。随后，我们研究了外部力量可以策略性地调节/影响用户更新的模型。我们考虑了外部力量可以引入额外代理以及修改其他代理成本结构的情况。我们描述并分析了一些通过顺序最优方式实现调节的策略。我们的模拟显示，泛化动态在定性和定量上都与传统HK动态不同。
英文摘要：
We study generalizations of the Hegselmann-Krause (HK) model for opinion dynamics, incorporating features and parameters that are natural components of observed social systems. The first generalization is one where the strength of influence depends on the distance of the agents' opinions. Under this setup, we identify conditions under which the opinions converge in finite time, and provide a qualitative characterization of the equilibrium. We interpret the HK model opinion update rule as a quadratic cost-minimization rule. This enables a second generalization: a family of update rules which possess different equilibrium properties. Subsequently, we investigate models in which a external force can behave strategically to modulate/influence user updates. We consider cases where this external force can introduce additional agents and cases where they can modify the cost structures for other agents. We describe and analyze some strategies through which such modulation may be possible in an order-optimal manner. Our simulations demonstrate that generalized dynamics differ qualitatively and quantitatively from traditional HK dynamics.
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