Exact time-dependent dynamics of discrete binary choice models

James Holehouse and José Moran

INET Oxford Working Papers from Institute for New Economic Thinking at the Oxford Martin School, University of Oxford

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 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 ! 1. 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.

Pages: 14 pages
Date: 2022-01
New Economics Papers: this item is included in nep-dcm and nep-ore
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Persistent link: https://EconPapers.repec.org/RePEc:amz:wpaper:2022-03

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