Irenaeus Wolff

The Effects of Punishment in Dynamic Public-Good Games

Considerable experimental evidence shows that although costly peer-punishment enhances cooperation in repeated public-good games, heavy punishment in early rounds leads to average period payoffs below the non-cooperative equilibrium benchmark. In an environment where past payoffs determine present contribution capabilities, this could be devastating. Groups could fall prey to a poverty trap or, to avoid this, abstain from punishment altogether. We show that neither is the case generally. By continuously contributing larger fractions of their wealth, groups with punishment possibilities exhibit increasing wealth increments, while increments fall when punishment possibilities are absent. Nonetheless, single groups do succumb to the above-mentioned hazards.

Retaliation and the role for punishment in the evolution of cooperation

Models of evolutionary game theory have shown that punishment may be an adaptive behaviour in environments characterised by a social-dilemma situation. Experimental evidence closely corresponds to this finding but questions the cooperation-enhancing effect of punishment if players are allowed to retaliate against their punishers. This study provides a theoretical explanation for the existence of retaliating behaviour in the context of repeated social dilemmas and analyses the role punishment can play in the evolution of cooperation under these conditions. We show a punishing strategy can pave the way for a partially cooperative equilibrium of conditional cooperators and defecting types and, under positive mutation rates, foster the cooperation level in this equilibrium by prompting reluctant cooperators to cooperate. However, when rare mutations occur, it cannot sustain cooperation by itself as punishment costs favour the spread of non-punishing cooperators.

Counterpunishment revisited: an evolutionary approach

Evolutionary game theory has shown that in environments characterised by a social-dilemma situation punishment may be an adaptive behaviour. Experimental evidence closely corresponds to this finding but yields contradictory results on the cooperation-enhancing effect of punishment if players are allowed to retaliate against their punishers. The present study sets out to examine the question of whether cooperation will still be part of an evolutionary stable strategy if we allow for counterpunishment opportunities in a theoretic model and tries to reconcile the seemingly contradictory findings from the laboratory. We find that the apparent contradictions can be explained by a difference in the number of retaliation stages employed (one vs many) and even small differences in the degree of retaliativeness.