The Social Cost of Cheap Pseudonyms

We consider the problems of societal norms for cooperation and reputation when it is possible to obtain cheap pseudonyms, something which is becoming quite common in a wide variety of interactions on the Internet. This introduces opportunities to misbehave without paying reputational consequences. A large degree of cooperation can still emerge, through a convention in which newcomers pay their dues by accepting poor treatment from players who have established positive reputations. One might hope for an open society where newcomers are treated well, but there is an inherent social cost in making the spread of reputations optional. We prove that no equilibrium can sustain significantly more cooperation than the dues-paying equilibrium in a repeated random matching game with a large number of players in which players have finite lives and the ability to change their identities, and there is a small but nonvanishing probability of mistakes. Although one could remove the ine...