The stranger on the Internet effect has been studied in relation to self-disclosure. Nonetheless, quantitative evidence about how people mentally represent and perceive strangers online is still missing. Given the dynamic development of web technologies, quantifying how much strangers can be considered suitable for pro-social acts such as self-disclosure appears fundamental for a whole series of phenomena ranging from privacy protection to fake news spreading. Using a modified and online version of the Ultimatum Game (UG), we quantified the mental representation of the stranger on the Internet effect and tested if people modify their behaviors according to the interactors' identifiability (i.e., reputation). A total of 444 adolescents took part in a 2 x 2 design experiment where reputation was set active or not for the two traditional UG tasks. We discovered that, when matched with strangers, people donate the same amount of money as if the other has a good reputation. Moreover, reputation significantly affected the donation size, the acceptance rate and the feedback decision making as well.