社交网络中的异步观点动力学
Asynchronous Opinion Dynamics in Social Networks
AI总结：
该研究聚焦社交网络变体的Hegselmann-Krause异步观点动力学模型，证明其在任意社交网络下均能收敛，推导了更优的收敛预期更新次数上界，并通过模拟验证存在匹配的渐近下界。
摘要：
社会中的观点传播决定着选举的走向、产品的成败以及政治或社会运动的影响力。Hegselmann-Krause模型是研究社交网络中此类观点形成过程的著名理论模型。与许多其他理论模型不同，它不会收敛至所有智能体达成一致观点的状态。相反，该模型假设人们当且仅当某一观点与自身观点接近时，才会认为该观点合理。系统最终会收敛至稳定状态：持有相同观点的智能体形成集群，不同集群中的智能体不会相互影响。\n我们聚焦于Hegselmann-Krause模型的社交网络变体，其中智能体通过社交网络连接，观点以迭代过程演化。当某个智能体被激活时，它会采纳与其观点相似的邻居的观点平均值。由此，智能体的有影响力邻居集合可能会随时间变化。据我们所知，带异步观点更新的社交Hegselmann-Krause系统此前仅在完全图作为社交网络的场景下被研究过。我们证明，这类带有随机智能体激活的观点动力学在任意社交网络下都能保证收敛。我们给出了收敛前预期观点更新次数的上界$\u27e8(n|E|^2 (\varepsilon/\delta)^2)$，其中$|E|$为社交网络的边数。对于完全社交网络，我们证明了上界为$\u27e8(n^3(n^2 + (\varepsilon/\delta)^2))$，这较此前最优的$\u27e8(n^9 (\varepsilon/\delta)^2)$上界有重大提升。我们还通过模拟实验补充了上界结果，实验表明存在渐近匹配的下界。
英文摘要：
Opinion spreading in a society decides the fate of elections, the success of products, and the impact of political or social movements. The model by Hegselmann and Krause is a well-known theoretical model to study such opinion formation processes in social networks. In contrast to many other theoretical models, it does not converge towards a situation where all agents agree on the same opinion. Instead, it assumes that people find an opinion reasonable if and only if it is close to their own. The system converges towards a stable situation where agents sharing the same opinion form a cluster, and agents in different clusters do not \mbox{influence each other.} We focus on the social variant of the Hegselmann-Krause model where agents are connected by a social network and their opinions evolve in an iterative process. When activated, an agent adopts the average of the opinions of its neighbors having a similar opinion. By this, the set of influencing neighbors of an agent may change over time. To the best of our knowledge, social Hegselmann-Krause systems with asynchronous opinion updates have only been studied with the complete graph as social network. We show that such opinion dynamics with random agent activation are guaranteed to converge for any social network. We provide an upper bound of $\mathcal{O}(n|E|^2 (\varepsilon/δ)^2)$ on the expected number of opinion updates until convergence, where $|E|$ is the number of edges of the social network. For the complete social network we show a bound of $\mathcal{O}(n^3(n^2 + (\varepsilon/δ)^2))$ that represents a major improvement over the previously best upper bound of $\mathcal{O}(n^9 (\varepsilon/δ)^2)$. Our bounds are complemented by simulations that indicate asymptotically matching lower bounds.
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