Cooperation without punishment

Abstract

A fundamental question in social and biological sciences is whether self-governance is possible when individual and collective interests are in conflict. Free riding poses a major challenge to self-governance, and a prominent solution to this challenge has been altruistic punishment. However, this solution is ineffective when counter-punishments are possible and when social interactions are noisy. We set out to address these shortcomings, motivated by the fact that most people behave like conditional cooperators-individuals willing to cooperate if a critical number of others do so. In our evolutionary model, the population contains heterogeneous conditional cooperators whose decisions depend on past cooperation levels. The population plays a repeated public goods game in a moderately noisy environment where individuals can occasionally commit mistakes in their cooperative decisions and in their imitation of the role models' strategies. We show that, under moderate levels of noise, injecting a few altruists into the population triggers positive reciprocity among conditional cooperators, thereby providing a novel mechanism to establish stable cooperation. More broadly, our findings indicate that self-governance is possible while avoiding the detrimental effects of punishment, and suggest that society should focus on creating a critical amount of trust to harness the conditional nature of its members.

Figure 1

The evolution of conditional cooperation. The x-axis represents the generation, the y-axis represents the cooperation level, and each color-coded trajectory depicts the evolutionary dynamics of cooperation under different experimental conditions, given $\beta =0.5$. a, Evolution of cooperation in the absence of altruists, given different percentages of cooperation decisions made in the first generation. b, Evolution of cooperation given different percentages of altruists present across generations when $w=1$.

Figure 2

Asymptotic cooperation levels. a, The x-axis represents the percentage of altruists, the y-axis represents the average cooperation level over the last 5000 generations out of 20,000 with $w=1$, with each color corresponding to a different level of noise, $\beta$. b, The same as (a) but for $w=0.5$ instead of $w=1$. c, The same as (a) but while varying w (x-axis) and fixing $\alpha =30\%$.

Figure 3

Distribution of the conditional cooperative criterion (CCC) values. Every altruists is born into the initial population with a conditional cooperative criterion $CC{C}_i=0$, while every conditional cooperator k is born with $CC{C}_i\sim \{0,\dots ,N\}$. The figure depicts the distribution of all CCC values in the 20,000th generation for different percentages of altruists ($\alpha$), different levels of noise ($\beta$), and different values of w. a, Results when $\alpha =30\%$, $\beta \in \{0.5,\infty \}$, and $w=1$. b, The same as (a) but for $w=0.5$ instead of $w=1$. c Results when $\alpha \in \{10\%,30\%\}$, $\beta =0.5$, and $w=1$. d, The same as (c) but for $w=0.5$ instead of $w=1$.