Participation costs can suppress the evolution of upstream reciprocity

Indirect reciprocity, one of the many mechanisms proposed to explain the evolution of cooperation, is the idea that altruistic actions can be rewarded by third parties. Upstream or generalized reciprocity is one type of indirect reciprocity in which individuals help someone if they have been helped by somebody else in the past. Although empirically found to be at work in humans, the evolution of upstream reciprocity is difficult to explain from a theoretical point of view. A recent model of upstream reciprocity, first proposed by Nowak and Roch (2007) and further analyzed by Iwagami and Masuda (2010), shows that while upstream reciprocity alone does not lead to the evolution of cooperation, it can act in tandem with mechanisms such as network reciprocity and increase the total level of cooperativity in the population. We argue, however, that Nowak and Roch's model systematically leads to non-uniform interaction rates, where more cooperative individuals take part in more games than less cooperative ones. As a result, the critical benefit-to-cost ratios derived under this model in previous studies are not invariant with respect to the addition of participation costs. We show that accounting for these costs can hinder and even suppress the evolution of upstream reciprocity, both for populations with non-random encounters and graph-structured populations.