The evolution of altruistic punishment

Abstract

Both laboratory and field data suggest that people punish noncooperators even in one-shot interactions. Although such "altruistic punishment" may explain the high levels of cooperation in human societies, it creates an evolutionary puzzle: existing models suggest that altruistic cooperation among nonrelatives is evolutionarily stable only in small groups. Thus, applying such models to the evolution of altruistic punishment leads to the prediction that people will not incur costs to punish others to provide benefits to large groups of nonrelatives. However, here we show that an important asymmetry between altruistic cooperation and altruistic punishment allows altruistic punishment to evolve in populations engaged in one-time, anonymous interactions. This process allows both altruistic punishment and altruistic cooperation to be maintained even when groups are large and other parameter values approximate conditions that characterize cultural evolution in the small-scale societies in which humans lived for most of our prehistory.

Figure 1

The evolution of cooperation is strongly affected by the presence of punishment. (a) The long run average frequency of cooperation (i.e., the sum of the frequencies of contributors and punishers) as a function of group size when there is no punishment (p = k = 0) for three different conflict rates, 0.075, 0.015, and 0.003. Group selection is ineffective unless groups are quite small. (b) When there is punishment (p = 0.8, k = 0.2), group selection can maintain cooperation in substantially larger groups.

Figure 2

The evolution of cooperation is strongly affected by rate of mixing between groups. (a) The long run average frequency of cooperation (i.e., the sum of the frequencies of contributors and punishers) as a function of group size when there is no punishment (p = k = 0) for three mixing rates, 0.002, 0.01, and 0.05. Group selection is ineffective unless groups are quite small. (b) When there is punishment (p = 0.8, k = 0.2), group selection can maintain cooperation in larger groups for all rates of mixing. However, at higher rates of mixing, cooperation does not persist in the largest groups.

Figure 3

The evolution of cooperation is sensitive to the cost of being punished (p). Here we plot the long run average frequency of cooperation with the base case cost of being punished (p = 0.8) and with a lower value of p. Lower values of p result in much lower levels of cooperation.

Figure 4

Punishment does not aid in the evolution of cooperation when the costs born by punishers are fixed, independent of the number of defectors in the group. Here we plot the long run average frequency of cooperation when the costs of punishing are proportional to the frequency of defectors (variable cost), fixed at a constant cost equal to the cost of cooperating (c), and when there is no punishment.