In the digital era, new socially shared realities and norms emerge rapidly, whether they are beneficial or harmful to our societies. Although these are emerging properties from dynamic interaction, most research has centered on static situations where isolated individuals face extant norms. We investigated how perceptual norms emerge endogenously as shared realities through interaction, using behavioral and fMRI experiments coupled with computational modeling. Social interactions fostered convergence of perceptual responses among people, not only overtly but also at the covert psychophysical level that generates overt responses. Reciprocity played a critical role in increasing the stability (reliability) of the psychophysical function within each individual, modulated by neural activity in the mentalizing network during interaction. These results imply that bilateral influence promotes mutual cognitive anchoring of individual views, producing shared generative models at the collective level that enable endogenous agreement on totally new targets–one of the key functions of social norms.