Why do the left and right sides of the vertebrate brain play different functions? Having a lateralized brain, in which each hemisphere carries out different functions, is ubiquitous among vertebrates. The different specialization of the left and right side of the brain may increase brain efficiency--and some evidence for that is reported here. However, lateral biases due to brain lateralization (such as preferences in the use of a limb or, in animals with laterally placed eyes, of a visual hemifield) usually occur at the population level, with most individuals showing similar direction of bias. Individual brain efficiency does not require the alignment of lateralization in the population. Why then are not left--and right-type individuals equally common? Not only humans, but most vertebrates show a similar pattern. For instance, in the paper I report evidence that most toads, chickens, and fish react faster when a predator approaches from the left. I argue that invoking individual brain efficiency (lateralization may increase fitness), evolutionary chance or direct genetic mechanisms cannot explain this widespread pattern. Instead, using concepts from mathematical theory of games, I show that alignment of lateralization at the population level may arise as an "evolutionarily stable strategy" when individually asymmetrical organisms must coordinate their behavior with that of other asymmetrical organisms. Thus, the population structure of lateralization may result from genes specifying the direction of asymmetries which have been selected under "social" pressures.