论文标题
与本地平均随机互动的意见动态的共识问题
The consensus problem for opinion dynamics with local average random interactions
论文作者
论文摘要
我们研究了基于代理模型的共识形成，它推广了最初由Krause \ cite {Kr}提出的，通过允许随机或随机关闭任何几个代理之间的通信通道，并在每个时间步骤中，根据代理人的观点的接近性，并具有概率定律。也就是说，我们考虑一个根据以下更新协议共享意见的代理体系。在时间$ t+1 $ the意见$ x_ {i} \ left（t+1 \ right）\ in \ weft [0,1 \右] $的代理$ i $的更新，以代理商的意见的加权平均值进行更新时间$ t+1 $以这样的方式随机更新，即可以选择代理$ j $属于此设置，独立于其他代理，其可能性是$ \ weft \ weft \ vert x_ {i} \ left（t \ priong）的非增加功能的函数 - 意见很亲密。我们证明该系统达成共识，即，随着时间往往无限，代理商的意见将呈指数迅速达到相同的价值。
We study the consensus formation for an agents based model, generalizing that originally proposed by Krause \cite{Kr}, by allowing the communication channels between any couple of agents to be switched on or off randomly, at each time step, with a probability law depending on the proximity of the agents' opinions. Namely, we consider a system of agents sharing their opinions according to the following updating protocol. At time $t+1$ the opinion $X_{i}\left( t+1\right) \in\left[ 0,1\right] $ of agent $i$ is updated at the weighted average of the opinions of the agents communicating with it at time $t.$ The weights model the confidence level an agent assign to the opinions of the other agents and are kept fixed by the system dynamics, but the set of agents communicating with any agent $i$ at time $t+1$ is randomly updated in such a way that the agent $j$ can be chosen to belong to this set independently of the other agents with a probability that is a non increasing function of $\left\vert X_{i}\left( t\right) -X_{j}\left( t\right) \right\vert .$ This condition models the fact that a communication among the agents is more likely to happen if their opinions are close. We prove that the system reaches consensus, i.e. as the time tends to infinity the agents' opinions will reach the same value exponentially fast.
