论文标题
混合的Hegselmann-Krause动力学
Mixed Hegselmann-Krause Dynamics
论文作者
论文摘要
原始的Hegselmann-Krause（HK）型号由一组〜$ n $的代理组成，其特征是他们的意见，其中一个数字是〜$ [0，1] $。 每个代理商（例如代理〜$ i $），通过采取所有邻居的平均意见来更新其意见〜$ x_i $，其意见与〜$ x_i $不同的代理商最多约为$ x_i $。 〜HK模型有两种类型：同步〜HK模型和异步〜HK模型。 对于同步模型，所有代理在每个时间步骤均同时更新他们的意见，而对于异步〜HK模型，只有一个代理在每个时间步骤中随机更新其意见。 本文关注的是〜HK意见动力学的变体，称为混合〜HK模型，在该模型中，每个代理都可以选择其固执的程度，并将其意见与每个更新中的邻居的平均意见相结合。 代理的固执程度可能会随着时间的流逝而不同和/或不同。 如果代理商在每次更新中的新意见是其邻居的平均意见，那么代理商并不是固执的或绝对开放的，如果其意见在更新时没有改变，则绝对固执。 在每个时间步骤中，所有代理都绝对开放的特定情况是同步〜HK模型。 相比之下，异步模型对应于特定情况，在每个时间步骤中，所有代理人绝对固执，除了一个绝对开放的态度均匀地选择的一个剂量。 我们首先表明同步〜HK模型的某些常见特性（例如有限时间收敛）不适合混合模型。 然后，我们研究了渐近稳定性保持的条件，或者可以为混合模型达成共识。
The original Hegselmann-Krause (HK) model consists of a set of~$n$ agents that are characterized by their opinion, a number in~$[0, 1]$. Each agent, say agent~$i$, updates its opinion~$x_i$ by taking the average opinion of all its neighbors, the agents whose opinion differs from~$x_i$ by at most~$ε$. There are two types of~HK models: the synchronous~HK model and the asynchronous~HK model. For the synchronous model, all the agents update their opinion simultaneously at each time step, whereas for the asynchronous~HK model, only one agent chosen uniformly at random updates its opinion at each time step. This paper is concerned with a variant of the~HK opinion dynamics, called the mixed~HK model, where each agent can choose its degree of stubbornness and mix its opinion with the average opinion of its neighbors at each update. The degree of the stubbornness of agents can be different and/or vary over time. An agent is not stubborn or absolutely open-minded if its new opinion at each update is the average opinion of its neighbors, and absolutely stubborn if its opinion does not change at the time of the update. The particular case where, at each time step, all the agents are absolutely open-minded is the synchronous~HK model. In contrast, the asynchronous model corresponds to the particular case where, at each time step, all the agents are absolutely stubborn except for one agent chosen uniformly at random who is absolutely open-minded. We first show that some of the common properties of the synchronous~HK model, such as finite-time convergence, do not hold for the mixed model. We then investigate conditions under which the asymptotic stability holds, or a consensus can be achieved for the mixed model.
