Exact time-dependent dynamics of discrete binary choice models
| Autor: | James Holehouse, José Moran |
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| Rok vydání: | 2022 |
| Předmět: |
History
Polymers and Plastics Statistical Mechanics (cond-mat.stat-mech) Computer Networks and Communications G.3 FOS: Physical sciences Industrial and Manufacturing Engineering Computer Science Applications Computer Science::Multiagent Systems FOS: Economics and business Artificial Intelligence Economics - Theoretical Economics Theoretical Economics (econ.TH) Business and International Management Condensed Matter - Statistical Mechanics Information Systems 82C31 (Primary) 82C23 (Primary) 60J28 (Secondary) |
| DOI: | 10.48550/arxiv.2201.09573 |
| Popis: | 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. Comment: 13 pages, 4 figures |
| Databáze: | OpenAIRE |
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