Individual humans, and members of diverse other species, show consistent differences in aggressiveness, shyness, sociability and activity. Such intraspecific differences in behaviour have been widely assumed to be non-adaptive variation surrounding (possibly) adaptive population-average behaviour. Nevertheless, in keeping with recent calls to apply Darwinian reasoning to ever-finer scales of biological variation, we sketch the fundamentals of an adaptive theory of consistent individual differences in behaviour. Our thesis is based on the notion that such ‘personality differences’ can be selected for if fitness payoffs are dependent on both the frequencies with which competing strategies are played and an individual's behavioural history. To this end, we review existing models that illustrate this and propose a game theoretic approach to analyzing personality differences that is both dynamic and state-dependent. Our motivation is to provide insights into the evolution and maintenance of an apparently common animal trait: personality, which has far reaching ecological and evolutionary implications.