Exact timedependent dynamics of discrete binary choice models
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 discrete agents and for any choice of parameters, recovering past results found in the limit N → ∞. We then solve extensions of the ant recruitment model for increasing asymmetry between the two choices. Finally, we provide an analytical timedependent solution to the standard voter model and a semianalytical solution to the vacillating voter model. Our results show that exact analytical timedependent solutions can be achieved for discrete choice models without invoking that the number of agents N are continuous or that both choices are symmetric, and additionally show how to practically use the analytics for fast evaluation of the resulting probability distributions.
 Publication:

Journal of Physics: Complexity
 Pub Date:
 September 2022
 DOI:
 10.1088/2632072X/ac8c78
 arXiv:
 arXiv:2201.09573
 Bibcode:
 2022JPCom...3c5005H
 Keywords:

 rationality;
 social choice;
 stochastic;
 master equation;
 time dependent;
 voter model;
 Condensed Matter  Statistical Mechanics;
 Economics  Theoretical Economics;
 82C31 (Primary);
 82C23 (Primary);
 60J28 (Secondary);
 G.3
 EPrint:
 13 pages, 4 figures