Cost of institutional incentives for promoting cooperation in $2\times2$ games and collective risk games

TL;DR

This paper analyzes the costs associated with institutional incentives designed to promote cooperation in $2\times2$ games and collective risk scenarios, using evolutionary dynamics and numerical simulations to understand their asymptotic behavior.

Contribution

It introduces a detailed analysis of the cost of incentives in promoting cooperation within fundamental game models under evolutionary dynamics, including new insights into their asymptotic limits.

Findings

Incentive costs vary with the strength of selection and approach specific limits under neutral drift and strong selection.

Numerical simulations reveal how parameters influence the cost functions' behavior.

The study provides a framework for understanding incentive costs in cooperation-promoting mechanisms.

Abstract

Prosocial behaviours have been extensively studied across multiple disciplines. Cooperation, requiring a personal cost for collective benefits, is widespread in nature and human society, having been explained through mechanisms such as kin selection, direct and indirect reciprocity, and network reciprocity. Institutional incentives, which reward cooperation and punish anti-social behaviour, offer a promising approach to fostering cooperation in groups of self-interested individuals. Focusing on general $2\times2$ games and the collective risk game (which is a fundamental model for climate action), we analyse the associated cost of providing incentives under evolutionary dynamics governed by Fermi's rule, exploring the asymptotic behaviour of the incentive cost functons in the limits of neutral drift and strong selection. We also implement numerical simulations to study how parameters such as the intensity of selection affect the behaviour of the aforementioned cost functions.