Exact time-dependent dynamics of discrete binary choice models

James Holehouse and Jos\'e Moran

Papers from arXiv.org

Abstract: 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 F\"ollmer'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.

Date: 2022-01, Revised 2022-02
New Economics Papers: this item is included in nep-dcm and nep-ore
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