This paper introduces a heterogeneous multidimensional bounded confidence (BC) opinion dynamics with random pairwise interactions, whereby each pair of agents accesses each other’s opinions with a specific probability. This revised model is motivated by the observation that the standard Hegselmann–Krause (HK) dynamics requires unrealistic all-to-all interactions at certain configurations. For this randomized BC opinion dynamics, regardless of initial opinions and positive confidence bounds, we show that the agents’ states converge to fixed final opinions in finite time almost surely and that the convergence rate follows a negative exponential distribution in mean square. Furthermore, we establish sufficient conditions for the heterogeneous BC opinion dynamics with random interactions to achieve consensus in finite time.

中文翻译：

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具有异质有限置信度和随机交互作用的多维意见动态


本文介绍了一种具有随机成对交互作用的异构多维有界置信度 （BC） 意见动态，其中每对代理都以特定的概率访问彼此的意见。这个修订后的模型是由以下观察结果驱动的：标准 Hegselmann-Krause （HK） 动力学需要在某些配置下进行不切实际的全对多交互。对于这种随机的 BC 意见动态，无论初始意见和积极置信边界如何，我们表明代理的状态几乎可以肯定地在有限时间内收敛到固定的最终意见，并且收敛率在均方中遵循负指数分布。此外，我们通过随机交互作用为异质 BC 意见动态建立了足够的条件，以在有限时间内达成共识。