Compulsory persistent cooperation in continuous public goods games

Yan Li, Xinsheng Liu*, Jens Christian Claussen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The public goods game (PGG), where players either contribute an amount to the common pool or do nothing, is a paradigm for exploring cooperative behaviors in biological systems, economic communities and other social systems. In many situations, including climate game and charity donations, any contribution, however large or small, should be welcome. Consequently, the conventional PGG is extended to a PGG with continuous strategy space, which still cannot escape the tragedy of commons without any enforcing mechanisms. Here we propose the persistent cooperation investment mechanisms based on continuous PGG, including single-group games, multi-group games with even investment, non-even investment and non-even investment with preference. We aim to reveal how these investment styles promote the average cooperation level in the absence of any other enforcing mechanisms. Simulations indicate that the multi-group game outperforms the single-group game. Among the multi-group game, non-even investment is superior to even investment, but inferior to non-even investment with preference. Our results may provide an explanation to the emergence of cooperative actions in continuous phenotypic traits based on inner competition and self-management without extrinsic enforcing mechanisms.

Original languageEnglish
Article number121767
JournalPhysica A: Statistical Mechanics and its Applications
Early online date11 Jun 2019
Publication statusPublished - 1 Oct 2019

Bibliographical note

© 2019, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

Funding: National Natural Science Foundation of China (61374183, 51535005), the Research Fund of State Key Laboratory of Mechanics and Control of Mechanical Structures (MCMS-I-0418K01, MCMS-I-0418Y01), the Fundamental Research Funds for the Central Universities (NC2018001, NP2019301, NJ2019002).


  • Evolution of cooperation
  • Evolutionary game theory
  • Public goods game


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