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Dreber, A., Rand, D. G., Fudenberg, D., & Nowak, M. A. (2008). Winners don/'t punish. Nature, 452(7185), 348–351.
Abstract: A key aspect of human behaviour is cooperation1, 2, 3, 4, 5, 6, 7. We tend to help others even if costs are involved. We are more likely to help when the costs are small and the benefits for the other person significant. Cooperation leads to a tension between what is best for the individual and what is best for the group. A group does better if everyone cooperates, but each individual is tempted to defect. Recently there has been much interest in exploring the effect of costly punishment on human cooperation8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23. Costly punishment means paying a cost for another individual to incur a cost. It has been suggested that costly punishment promotes cooperation even in non-repeated games and without any possibility of reputation effects10. But most of our interactions are repeated and reputation is always at stake. Thus, if costly punishment is important in promoting cooperation, it must do so in a repeated setting. We have performed experiments in which, in each round of a repeated game, people choose between cooperation, defection and costly punishment. In control experiments, people could only cooperate or defect. Here we show that the option of costly punishment increases the amount of cooperation but not the average payoff of the group. Furthermore, there is a strong negative correlation between total payoff and use of costly punishment. Those people who gain the highest total payoff tend not to use costly punishment: winners don't punish. This suggests that costly punishment behaviour is maladaptive in cooperation games and might have evolved for other reasons.
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Ohtsuki, H., Iwasa, Y., & Nowak, M. A. (2009). Indirect reciprocity provides only a narrow margin of efficiency for costly punishment. Nature, 457(7225), 79–82.
Abstract: Indirect reciprocity1, 2, 3, 4, 5 is a key mechanism for the evolution of human cooperation. Our behaviour towards other people depends not only on what they have done to us but also on what they have done to others. Indirect reciprocity works through reputation5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. The standard model of indirect reciprocity offers a binary choice: people can either cooperate or defect. Cooperation implies a cost for the donor and a benefit for the recipient. Defection has no cost and yields no benefit. Currently there is considerable interest in studying the effect of costly (or altruistic) punishment on human behaviour18, 19, 20, 21, 22, 23, 24, 25. Punishment implies a cost for the punished person. Costly punishment means that the punisher also pays a cost. It has been suggested that costly punishment between individuals can promote cooperation. Here we study the role of costly punishment in an explicit model of indirect reciprocity. We analyse all social norms, which depend on the action of the donor and the reputation of the recipient. We allow errors in assigning reputation and study gossip as a mechanism for establishing coherence. We characterize all strategies that allow the evolutionary stability of cooperation. Some of those strategies use costly punishment; others do not. We find that punishment strategies typically reduce the average payoff of the population. Consequently, there is only a small parameter region where costly punishment leads to an efficient equilibrium. In most cases the population does better by not using costly punishment. The efficient strategy for indirect reciprocity is to withhold help for defectors rather than punishing them.
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Nowak, M. A., & Sigmund, K. (1992). Tit for tat in heterogeneous populations. Nature, 355, 250–253.
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