The logic of reprobation: assessment and action rules for indirect reciprocation

Abstract

Ever since image-based models for indirect reciprocity were introduced, the relative merits of scoring vs. standing have been discussed to find out how important it is to differentiate between justified and non-justified defections. This is analogous to the question whether punishment can sustain cooperation even when it is costly. We show that an answer to this question can depend on details of the model, for instance concerning the probability distribution of the number of interactions experienced per player. We use extensive individual-based simulations to compare scoring, standing and other forms of assessing defections, and show that several forms of indirect reciprocation can robustly sustain cooperation. By most standards, standing is better than scoring, but nevertheless scoring is able to sustain cooperation in the presence of errors. The model presented here is based on three specifications: each player has a personal list of images of all co-players, a specific way of judging an observed situation, and a specific strategy to decide whether to cooperate or not.