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Abstract

The emergence and maintenance of punishment to protect the commons
remains an open puzzle in social and biological sciences. Even in societies
where pro-social punishing is common, some individuals seek to cheat the
system if they see a chance to do so—and public goods are often maintained
in spite of cheaters who do not contribute.We present a model accounting for
all possible strategies in a public goods game with punishment. While most
models of punishment restrict the set of possible behaviours, excluding seemingly
paradoxical anti-social strategies from the start, we show that these
strategies can play an important role in explaining large-scale cooperation
as observed in human societies. We find that coordinated punishment can
emerge from individual interactions, but the stability of the associated institutions
is limited owing to anti-social and opportunistic behaviour. In
particular, coordinated anti-social punishment can undermine cooperation
if individuals cannot condition their behaviour on the existence of institutions
that punish. Only when we allow for observability and conditional behaviours
do anti-social strategies no longer threaten cooperation. This is due
to a stable coexistence of a minority supporting pro-social institutions and
those who only cooperate if such institutions are in place. This minority of
supporters is enough to guarantee substantial cooperation under a wide
range of conditions. Our findings resonate with the empirical observation
that public goods are resilient to opportunistic cheaters in large groups of
unrelated individuals. They also highlight the importance of letting evolution,
and not modellers, decide which strategies matter.