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 that 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" buy 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 inefficiency of mistreating newcomers by disallowing anonymity, this is not practical or desirable in a wide variety of transactions. We discuss the use of entry fees, which permits newcomers to be trusted but excludes some players with low payoffs, thus introducing a different inefficiency. We also discuss the use of free but unreplaceable pseudonyms, and describe a mechanism that implements them using standard encryption techniques, which could be practically implemented in electronic transactions.