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.