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arXiv 2402.01940physics.soc-ph
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作为动力系统的广义命名博弈与贝叶斯命名博弈

Generalized Naming Game and Bayesian Naming Game as Dynamical Systems

Gionni Marchetti

AI总结:

本研究将β模型与贝叶斯命名博弈作为动力系统分析,发现β模型存在分岔点为1/3的非通有分岔并形成椭圆弧状吸引不变流形,同时提出用logistic函数建模贝叶斯学习概率,无需强假设即可证明BNG不动点存在。

摘要:

我们将β模型(β-NG)和贝叶斯命名博弈(Bayesian Naming Game, BNG)作为动力系统展开研究。通过对与β模型相关的动力系统开展线性稳定性分析,我们证明存在一个非通有分岔,其分岔点β_c=1/3。当β穿过β_c时,孤立不动点的稳定性发生改变,进而产生一个一维不动点流形。值得注意的是,该吸引不变流形构成一段椭圆弧。在BNG的研究语境下,我们提出将贝叶斯学习概率p_A和p_B建模为logistic函数。这种建模方法使我们能够在无需依赖p_A=p_B=p(其中p为常数)这一过强假设的前提下,证明不动点的存在性。

英文摘要:

We study the $β$-model ($β$-NG) and the Bayesian Naming Game (BNG) as dynamical systems. By applying linear stability analysis to the dynamical system associated with the $β$-model, we demonstrate the existence of a non-generic bifurcation with a bifurcation point $β_c = 1/3$. As $β$ passes through $β_c$, the stability of isolated fixed points changes, giving rise to a one-dimensional manifold of fixed points. Notably, this attracting invariant manifold forms an arc of an ellipse. In the context of the BNG, we propose modeling the Bayesian learning probabilities $p_A$ and $p_B$ as logistic functions. This modeling approach allows us to establish the existence of fixed points without relying on the overly strong assumption that $p_A = p_B = p$, where $p$ is a constant.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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