论文标题
具有嘈杂相互作用的非线性意见动力学的相变
Phase Transition of a Non-Linear Opinion Dynamics with Noisy Interactions
论文作者
论文摘要
在几种真实的\ emph {多代理系统}（MAS）中，已经观察到，仅实现了\ emph {亚稳定共识}的较弱形式，其中大多数特工就某些意见达成共识，而其他观点则继续受到（小）少数人的支持。在这项工作中，我们通过考虑二进制环境中著名的\未确定的动力学来调查对复杂（非线性）\ emph {意见动力学}的亚稳定共识的一步。 我们提出了一种简单的均匀噪声形式，其中每个消息都可以将概率$ p $更改为另一个消息，我们证明了\ emph {m ostostable共识}的持久性在$ p = \ frac 16 $中经历\ emph {apepress transition}。详细说明，在此阈值之下，我们证明了系统以高概率到达的概率，其中绝大多数代理商不断支持多项式时间的相同意见。此外，这种意见被证明是最初的多数意见，每当初始偏见略大于其标准偏差时。相反，相反，高于阈值，我们表明，关于最初多数意见的信息在最大的时间内“丢失”，即使初始偏见是最大的，即使是最大程度地间隔。 \ emph {subborn}方式。
In several real \emph{Multi-Agent Systems} (MAS), it has been observed that only weaker forms of\emph{metastable consensus} are achieved, in which a large majority of agents agree on some opinion while other opinions continue to be supported by a (small) minority of agents. In this work, we take a step towards the investigation of metastable consensus for complex (non-linear) \emph{opinion dynamics} by considering the famous \undecided dynamics in the binary setting, which is known to reach consensus exponentially faster than the \voter dynamics. We propose a simple form of uniform noise in which each message can change to another one with probability $p$ and we prove that the persistence of a \emph{metastable consensus} undergoes a \emph{phase transition} for $p=\frac 16$. In detail, below this threshold, we prove the system reaches with high probability a metastable regime where a large majority of agents keeps supporting the same opinion for polynomial time. Moreover, this opinion turns out to be the initial majority opinion, whenever the initial bias is slightly larger than its standard deviation.On the contrary, above the threshold, we show that the information about the initial majority opinion is "lost" within logarithmic time even when the initial bias is maximum.Interestingly, using a simple coupling argument, we show the equivalence between our noisy model above and the model where a subset of agents behave in a \emph{stubborn} way.
