Enhancement of cooperation by giving high-degree neighbors more help

TL;DR

This study investigates how preferential assistance based on neighbors' degree influences cooperation in a donation game, revealing an optimal level of assistance that maximizes cooperative behavior.

Contribution

It introduces a model where individuals distribute benefits unevenly based on neighbors' degree, identifying an optimal assistance level to promote cooperation.

Findings

Existence of an optimal positive exponent $oldsymbol{ extalpha}$ for maximum cooperation.

Preferential assistance to high-degree neighbors enhances cooperation.

Over-assistance can reduce overall cooperation.

Abstract

In this paper, we study the effect of preferential assistance on cooperation in the donation game. Cooperators provide benefits to their neighbors at some costs. Defectors pay no cost and do not distribute any benefits. The total contribution of a cooperator is fixed and he/she distributes his/her contribution unevenly to his/her neighbors. Each individual is assigned a weight that is the power of its degree, where the exponent $\alpha$ is an adjustable parameter. The amount that cooperator $i$ contributes to a neighbor $j$ is proportional to $j$'s weight. Interestingly, we find that there exists an optimal value of $\alpha$ (which is positive), leading to the highest cooperation level. This phenomenon indicates that, to enhance cooperation, individuals could give high-degree neighbors more help, but only to a certain extent.