Abstract Mirror images simulating social partners that cooperated or defected have been used as an experimental method to test the hypothesis that, while inspecting a predator, pairs of fish play a conditional strategy, Tit for Tat, in an iterated version of the Prisoner’s Dilemma game. Using this method, we found that predator inspection was more likely to occur when the mirror image was visible on the left rather than on the right side of mosquitofish, Gambusia holbrooki. The same occurred even when a videorecorded stimulus presentation was used, in which sequences of the predator were mixed with their mirror-image equivalents, thus showing that the asymmetry was not due to behavioural or morphological asymmetries of the predator itself. Moreover, irrespective of whether they were tested with a cooperative (parallel mirror) or a defecting (angled mirror) partner, mosquitofish drew closer to the predator when the mirror was on their left side. These findings suggest that the images seen on the right and left sides by a fish may evoke different types of social behaviour, probably because of differing modes of analysis of perceptual information carried out by the left and right sides of the brain; accurate control and balancing of the side of presentation of visual stimuli during behavioural experiments thus appears to be crucial.