Via freedom to coercion: the emergence of costly punishment

Abstract

In human societies, cooperative behavior in joint enterprises is often enforced through institutions that impose sanctions on defectors. Many experiments on so-called public goods games have shown that in the absence of such institutions, individuals are willing to punish defectors, even at a cost to themselves. Theoretical models confirm that social norms prescribing the punishment of uncooperative behavior are stable-once established, they prevent dissident minorities from spreading. But how can such costly punishing behavior gain a foothold in the population? A surprisingly simple model shows that if individuals have the option to stand aside and abstain from the joint endeavor, this paves the way for the emergence and establishment of cooperative behavior based on the punishment of defectors. Paradoxically, the freedom to withdraw from the common enterprise leads to enforcement of social norms. Joint enterprises that are compulsory rather than voluntary are less likely to lead to cooperation.

Figure 1

Punishment and abstaining in joint effort games. (a) Simulations of finite populations consisting of four types of players show that after some initial oscillations, punishers usually dominate the population. In longer runs, their regime can occasionally break down, because cooperators invade by neutral drift, but after another series of oscillations punishers will emerge again. The transient oscillations generally display a rock-paper-scissors-like succession of cooperators, defectors and non-participants. When non-participants are frequent, groups are small, and punishing therefore is less costly, so that punishers have a chance to invade. (b) If participation is compulsory (no non-participants), defectors take over in the long run, even if the population consisted initially of punishers. Parameter values are M = 100, N = 5, r = 3, σ = 1, γ = 0.3, β = 1, c = 1, μ = 0.01.c

Figure 2

Stationary probability distributions, transition probabilities and fixation times can be computed analytically for sufficiently small mutation rates, if we assume that players update their strategies according to some specified rule. (Here, we use a Moran process with selection strength s = 0.249, see (17)). The dynamics is reduced to transitions between homogeneous population states consisting entirely of cooperators (C), defectors (D), non-participants (N) or punishers (P). The transition probabilities ρ denote the probabilities that a single mutant takes over, the conditional fixation time t indicates the average number of periods required for a single mutant to reach fixation, provided that the mutant takes over. a voluntary participation in the joint effort game with punishment, parameter values N = 5, r = 3, σ = 1, γ = 0.3, β = 1, c = 1, M = 100. b compulsory participation in a joint effort game with punishment, for the same parameter values.

Figure 3

Punishment is best directed at defectors only. a Same as in Fig. 2a, but without punishers. The three remaining strategies supersede each other in a rock-paper-scissors type of cycle. b Same as in Fig. 2a, but assuming that punishers equally punish the non-participants. This makes it more difficult for punishers to dominate.