Probabilistic sharing solves the problem of costly punishment

TL;DR

This paper proposes probabilistic sharing of sanctioning responsibilities in public goods games, transforming the dynamics to promote cooperation and resolve the costly punishment dilemma through a novel, emotionally inspired approach.

Contribution

It introduces probabilistic sanctioning as a simple method to distribute punishment duties, addressing the second-order free-rider problem and enhancing cooperation in public goods scenarios.

Findings

Probabilistic sanctioning creates a coordination game with stable cooperation.

Structured populations exhibit pattern formation supporting cooperation.

The approach mitigates the second-order free-rider problem.

Abstract

Cooperators that refuse to participate in sanctioning defectors create the second-order free-rider problem. Such cooperators will not be punished because they contribute to the public good, but they also eschew the costs associated with punishing defectors. Altruistic punishers - those that cooperate and punish - are at a disadvantage, and it is puzzling how such behaviour has evolved. We show that sharing the responsibility to sanction defectors rather than relying on certain individuals to do so permanently can solve the problem of costly punishment. Inspired by the fact that humans have strong but also emotional tendencies for fair play, we consider probabilistic sanctioning as the simplest way of distributing the duty. In well-mixed populations the public goods game is transformed into a coordination game with full cooperation and defection as the two stable equilibria, while in structured populations pattern formation supports additional counterintuitive solutions that are reminiscent of Parrondo's paradox.