New Publication on Time-Dependent Solutions to Kirman's Ants

Alongside Dr. José Moran at the University of Oxford, we have a new publication on an exact time-dependent solution to Kirman’s model of ant rationality. Kirman’s model of ant rationality is seminal, as it showed how coalescent behaviour of ants (or decision making agents) can arise purely from endogenous effects alone, without the need for changes or bias in the external state of the system. Here we show that one can solve the model exactly in time using the method of generating functions, and that one can determine the eigenvalues defining the problem by enforcing physicality constraints on the generating function. We further show this for increasing degrees of asymmetry in the dynamics of the ants. You can access the paper here.

Caption: examples of (a) random switching dominating recruitment, (b) “equal” contribution from random switching and recruitment, and (c) domination of recruitment.