The evolution of cooperation under cheap pseudonyms

A wide variety of interactions on the Internet are characterized by the availability of cheap pseudonyms, where users can obtain new identities freely or at a low cost. Due to the availability of cheap pseudonyms, incentive schemes that are based on reward and punishment are vulnerable to the whitewashing attack, where users continuously discard their old identity and acquire a new one to escape the consequences of their bad behavior. In this paper, we study the implications of the whitewashing attack from an evolutionary perspective. Not surprisingly, the whitewashing attack degrades the evolutionary stability of strategies that are otherwise stable. In particular, the tit-for-tat strategy and its variant, probabilistic TFT, are not stable against white-washers, unless identity costs are sufficiently large. In addition, we extend the indirect reciprocity model and find that discriminators can defeat whitewashers only if the probability to cooperate with strangers is small enough, which in turn degrades social welfare.