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Abstract

Punishment of free-riders is generally viewed as an important factor in promoting
cooperation. But since it is often costly to sanction exploiters, the emergence of such a behavior
and its stability raise interesting problems. Players who do not contribute to the sanctions,
but profit from the increased level of cooperation caused by them, act as “second-order
exploiters” and threaten the joint enterprise. In this paper, we review the role of voluntary
participation in establishing and upholding cooperation with or without punishment. In particular,
we deal with two distinct forms of punishment, namely peer punishment and pool
punishment, and compare their stability and their efficiency. The emergence and upkeep
of collaborative undertakings can strongly depend on whether participation is voluntary or
mandatory. The possibility to opt out of a joint enterprise often helps in curbing exploiters
and boosting pro-social behavior.