Social and Cognitive Networks Academic Research Center, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.
Chaos. 2011 Jun;21(2):025115. doi: 10.1063/1.3598450.
We investigate consensus formation and the asymptotic consensus times in stylized individual- or agent-based models, in which global agreement is achieved through pairwise negotiations with or without a bias. Considering a class of individual-based models on finite complete graphs, we introduce a coarse-graining approach (lumping microscopic variables into macrostates) to analyze the ordering dynamics in an associated random-walk framework. Within this framework, yielding a linear system, we derive general equations for the expected consensus time and the expected time spent in each macro-state. Further, we present the asymptotic solutions of the 2-word naming game and separately discuss its behavior under the influence of an external field and with the introduction of committed agents.
我们研究了在基于个体或代理的简化模型中达成共识的形成和渐近共识时间，其中通过带有或不带有偏差的成对谈判来实现全球共识。考虑一类基于个体的有限完整图模型，我们引入一种粗粒化方法（将微观变量聚类为宏观状态）来分析相关随机游走框架中的排序动力学。在这个框架内，得到一个线性系统，我们推导出了用于预期共识时间和每个宏观状态所花费时间的期望的一般方程。此外，我们还给出了 2 字命名游戏的渐近解，并分别讨论了在外部场影响下和引入承诺代理时的行为。
