Indirect reward and punishment - their payoff

Ule et al. examine indirect reciprocity, which in widespread in human culture - rewarding those we know have been kind to others or punishing those we know have been unkind to others. They devise a game to show that cooperation is enhanced best by a system in which both indirect rewards and indirect punishment can occur. Here is their experimental setup, followed by their abstract:

Our experimental design builds on the so-called "indirect helping game". In total, 140 participants are repeatedly (100 rounds), anonymously, and randomly matched into donor-recipient pairs. Because roles are determined randomly, participants will typically be the donor in approximately half of the rounds. In the indirect helping game, only donors make decisions. In any round, each donor first observes the recipient’s recent behavior in the role of donor and then decides whether to "help" the recipient or to "pass." Helping is costly for the donor and beneficial for the recipient, with the benefits exceeding the costs. In earlier experiments, indirect punishment was not available as an option, a restriction that is arguably not a realistic feature of human interactions. In our experiment, the donor can choose to "hurt" the recipient instead of passing or helping. Hurting is costly for the donor, but we vary its impact on the receiver. We conducted two treatments that differ only in this impact, which allows us to isolate the effect of indirect punishment on the payoff performance of different types of behavior. In our main treatment [harmful punishment (HP)], a hurt recipient loses 250 units of our experimental money, "francs." In the control treatment [symbolic punishment (SP)], a hurt recipient loses or earns no francs. We say that punishment is harmful in HP but only symbolic in SP. In both treatments, the donor loses 50 francs for hurting or 200 francs for helping, and the recipient earns 250 francs when he or she receives help. Passing does not affect either player’s payoff. In both treatments the recipient observes the donor’s action. Treatment SP is a control for HP, because it identifies differences in behavior between environments where indirect punishment has material consequences for the recipient and where it does not, while holding all other parameters constant across treatments.

the final conclusions, from the abstract:

We find that if unkind strangers cannot be punished, defection earns most. If they can be punished, however, then indirect rewarding earns most. Indirect punishment plays this important role, even if it gives a low payoff and is rarely implemented.