Behavioural lateralization is widespread. Yet, a fundamental question remains, how can lateralization be evolutionary stable when individuals lateralized in one direction often significantly outnumber individuals latera-lized in the opposite direction? A recently developed game theory model predicts that fitness consequences which occur during intraspecific interactions may be driving population-level lateralization as an evolutionary stable strategy. This model predicts that: (i) minority-type individuals exist because they are more likely to adopt unpredictable fighting behaviours during competitive interactions (e.g. fighting); and (ii) majority-type individuals exist because there is a fitness advantage in having their biases synchronized with other conspecifics during interactions that require coordination (e.g. mating). We tested these predictions by investigating biases in giant Australian cuttlefish during fighting and mating interactions. During fighting, most male cuttlefish favoured the left eye and these males showed higher contest escalation; but minority-type individuals with a right-eye bias achieved higher fighting success. During mating interactions, most male cuttlefish favoured the left eye to inspect females. Furthermore, most male cuttlefish approached the female's right side during a mating attempt and these males achieved higher mating success. Our data support the hypothesis that population-level biases are an evolutionary consequence of the fitness advantages involved in intraspecific interactions.