Initial Analysis of a Simple Numerical Model that Exhibits Antifragile Behavior

Abstract

I present a simple numerical model based on iteratively updating subgroups of a population, individually modeled by nonnegative real numbers, by a constant decay factor; however, at each iteration, one group is selected to instead be updated by a constant growth factor. I discover a relationship between these variables and their respective probabilities for a given subgroup, summarized as the variable $c$. When $c>1$, the subgroup is found to tend towards behaviors reminiscent of antifragility; when at least one subgroup of the population has $c\ge1$, the population as a whole tends towards significantly higher probabilities of "living forever," although it may first suffer a drop in population size as less robust, fragile subgroups "die off." In concluding, I discuss the limitations and ethics of such a model, notably the implications of when an upper limit is placed on the growth constant, requiring a population to facilitate an increase in the decay factor to lessen the impact of periods of failure.