A generalized public goods game with coupling of individual ability and project benefit

TL;DR

This paper extends the public goods game by integrating individual ability and project benefits, analyzing how parameter coupling influences cooperation evolution and group size preferences.

Contribution

It introduces a generalized model coupling individual ability and project benefits, revealing their effects on cooperation dynamics and group size distribution.

Findings

Increasing individual benefit limit promotes cooperation.

Higher contribution limits inhibit cooperation.

Critical project benefit threshold maximizes cooperation.

Abstract

Facing a heavy task, any single person can only make a limited contribution and team cooperation is needed. As one enjoys the benefit of the public goods, the potential benefits of the project are not always maximized and may be partly wasted. By incorporating individual ability and project benefit into the original public goods game, we study the coupling effect of the four parameters, the upper limit of individual contribution, the upper limit of individual benefit, the needed project cost and the upper limit of project benefit on the evolution of cooperation. Coevolving with the individual-level group size preferences, an increase in the upper limit of individual benefit promotes cooperation while an increase in the upper limit of individual contribution inhibits cooperation. The coupling of the upper limit of individual contribution and the needed project cost determines the critical point of the upper limit of project benefit, where the equilibrium frequency of cooperators reaches its highest level. Above the critical point, an increase in the upper limit of project benefit inhibits cooperation. The evolution of cooperation is closely related to the preferred group-size distribution. A functional relation between the frequency of cooperators and the dominant group size is found.