Sustainable institutionalized punishment requires elimination of second-order free-riders

TL;DR

This paper demonstrates that sustainable institutionalized punishment in structured populations requires the sanctioning of second-order free-riders to prevent their dominance and ensure the stability of cooperation.

Contribution

It reveals that punishing second-order free-riders is essential for the sustainability of pool-punishment in structured populations, highlighting a phase transition in cooperation dynamics.

Findings

Pool-punishment is sustainable only when second-order free-riders are sanctioned.

A discontinuous phase transition leads to widespread sustainability.

Sanctioning second-order free-riders prevents their dominance over cooperators.

Abstract

Although empirical and theoretical studies affirm that punishment can elevate collaborative efforts, its emergence and stability remain elusive. By peer-punishment the sanctioning is something an individual elects to do depending on the strategies in its neighborhood. The consequences of unsustainable efforts are therefore local. By pool-punishment, on the other hand, where resources for sanctioning are committed in advance and at large, the notion of sustainability has greater significance. In a population with free-riders, punishers must be strong in numbers to keep the "punishment pool" from emptying. Failure to do so renders the concept of institutionalized sanctioning futile. We show that pool-punishment in structured populations is sustainable, but only if second-order free-riders are sanctioned as well, and to a such degree that they cannot prevail. A discontinuous phase transition leads to an outbreak of sustainability when punishers subvert second-order free-riders in the competition against defectors.