Abstract
Individuals of a species cope with environmental variability through
behavioral adjustments driven by individuals’ responsiveness to
environmental stimuli. Three key empirical observations have been made
for many animal species: The coexistence of different degrees of
responsiveness within one species; the consistency of an individual’s
degree of responsiveness across time; and the correlation of an
individual’s degree of responsiveness across contexts. Taking up key
elements of existing approaches, we provide one unifying explanation for
all three observations, by identifying a unique evolutionarily stable
strategy of an appropriately defined game within a stochastic
environment that has all three features. Coexistence is explained by a
form of negative frequency dependence. Consistency and correlation is
explained through potentially small, individual, differences of states
animals have and the resulting differential advantages they can get from
it. Our results allow us to identify a variety of testable implications.