离散二元选择模型的精确时变动力学
Exact time-dependent dynamics of discrete binary choice models
摘要：
我们提供了一个通用的方法来找到完整的动态解决方案的二元决策模型的相互作用。在这些模型中，代理遵循随机演化，他们必须考虑到他们的同伴的选择，在两个可能的选择之间进行选择。我们说明了我们的方法解决Kirman和Föllmer的蚂蚁招聘模型的任何数量$N$的代理和任何选择的参数，恢复过去的结果中发现的限制$N\to \infty$。然后，我们解决扩展的蚂蚁招聘模型增加两个选择之间的不对称性。最后，我们提供了一个分析的时间依赖解决方案的标准选民模型和半解析解决方案的摇摆选民模型。
英文摘要：
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.
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