AI 中文总结
该研究提出一种演化网络上的观点动态模型，将其表征为带双状态顶点的有向优先连接网络或大象随机游走变体，分析了固定与增长样本量下的渐近性质。
AI 中文摘要
我们研究演化网络上的观点动态、社会学习或基于同行评审的市场经济模型，其中：i）前N个智能体每个任意采用两种可用观点之一；ii）对于n≥N，第(n+1)个智能体到达时，从过往智能体中有放回地抽取大小为kₙ的样本，第i个智能体（i≤n）被纳入样本的概率与其先前被抽取且意见一致的次数成正比。随后第(n+1)个智能体根据：i）符合两种观点的样本智能体的比例；ii）包含记忆参数和相当通用的强化函数的随机更新规则，决定采用哪种观点。我们研究两种场景：i）kₙ=k随n保持固定；ii）kₙ随n以合适速率增长。该模型可表示为每个顶点具有两种可能状态之一且所有边有向的演化优先连接网络，也可被视为著名的大象随机游走的变体。我们研究该随机过程的渐近性质，特别是几乎必然收敛，以及在固定样本量情况下，每种观点的相对优势、影响资本和整体网络活动的二阶波动。
英文摘要
We study a model of opinion dynamics / social learning / peer-review-based market economics on an evolving network, wherein i) each of the first $N$ agents adopts one of two available opinions arbitrarily, and ii) the $(n+1)$-st agent, for $n\geqslant N$, upon arrival, draws a sample of size $k_{n}$, with replacement, from the past agents, such that the $i$-th agent (for $i\leqslant n$) is included in the sample with probability proportional to the number of times they were previously sampled and agreed with. The $(n+1)$-st agent then decides which opinion to adopt i) based on the proportion of sampled agents conforming to each of the two opinions, and ii) according to a stochastic update rule that involves a memory parameter and a rather general reinforcement function. We study both i) the scenario where $k_{n}=k$ remains fixed with $n$, and ii) the scenario where $k_{n}$ grows at a suitable rate with $n$. This model can be represented as an evolving preferential attachment network wherein each vertex is endowed with one of two possible states, and all edges are directed. It can also be framed as a variant of the celebrated elephant random walk. We study the asymptotics of this stochastic process -- in particular, the almost sure convergence, and in case of fixed sample sizes, second order fluctuations, of the relative dominance of each opinion, the influence capital and overall network activity.
Comments34 pages, rest bibliography. 2 images
