论文标题
离散二进制选择模型的确切时间相关动力学
Exact time-dependent dynamics of discrete binary choice models
论文作者
论文摘要
我们提供了一种通用方法，可以找到与相互作用的二进制决策模型的完整动力解决方案。在这些模型中，代理遵循随机演变，必须考虑到同龄人的选择，必须在两个可能的选择之间进行选择。我们通过为任何数字$ n $的代理和任何选择参数求解Kirman和Föllmer的蚂蚁招聘模型来说明我们的方法，从而恢复了在限制$ n \ to \ \ hyfty $中发现的过去结果。然后，我们解决了蚂蚁募集模型的扩展，以增加两种选择之间的不对称性。最后，我们为标准选民模型提供了分析时间依赖的解决方案，并为液态选民模型提供了半分析解决方案。
We provide a generic method to find full dynamical solutions to binary decision models with interactions. In these models, agents follow a stochastic evolution where they must choose between two possible choices by taking into account the choices of their peers. We illustrate our method by solving Kirman and Föllmer's ant recruitment model for any number $N$ of agents and for any choice of parameters, recovering past results found in the limit $N\to \infty$. We then solve extensions of the ant recruitment model for increasing asymmetry between the two choices. Finally, we provide an analytical time-dependent solution to the standard voter model and a semi-analytical solution to the vacillating voter model.
