Cooperation dilemmas in multi-stage public goods games with finite populations

Yewei Tao, Xiaoqian Zhao, Wenhua Li, Kaipeng Hu and Lei Shi

Chaos, Solitons & Fractals, 2025, vol. 199, issue P2

Abstract: Cooperation in the real world is often based on continuous inputs in multiple stages, and the realization of cooperative outcomes depends on individual strategic choices in multiple successive stages. However, this mechanism of stage benefit accumulation and delayed distribution may compress the viability of cooperation and exacerbate the evolutionary pressure faced by cooperators. In this paper, we construct a two-stage public goods game model based on finite populations, and examine the effects of different selection intensities and stage synergy factors on the evolution of the system. It is found that under the setting of cumulative gains and delayed allocation, it is difficult for cooperators to resist the joint exploitation by defectors at different stages, and the system is more inclined to evolution to a mixed-strategy pattern dominated by first-stage cooperation only. It is difficult to change the cooperation disadvantage by enhancing the first-stage synergies alone, and it is also difficult to realize the full cooperation steady state by enhancing the two-stage synergy factors at the same time. In contrast, weak selection or smaller group sizes can help alleviate the pressure of strategic exploitation and provide a narrow space for cooperation.

Keywords: Multi-stage public goods game; Evolution of cooperation; Finite population; Group size (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077925007271
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:199:y:2025:i:p2:s0960077925007271

DOI: 10.1016/j.chaos.2025.116714

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().