Cooperation in public goods game does not require assortment and depends on population density

Area of Science:

• Evolutionary Game Theory
• Mathematical Biology
• Social Dilemmas

Background:

• The threshold public goods game models non-linear social dilemmas.
• Cooperator-defector coexistence is common under structured deme models.
• Previous models often assume population structure, limiting generalizability.

Purpose of the Study:

• To develop a dynamical model for N-player games without deme structure.
• To investigate cooperation dynamics in well-mixed populations.
• To analyze the effects of population density and fluctuations on cooperation.

Main Methods:

• Developed a general N-player dynamical model for games without deme structure.
• Analyzed the deterministic limit, revealing replicator dynamics.
• Incorporated density dependence and fluctuations into the model.
• Employed analytical and numerical methods for investigation.

Main Results:

• The model replicates structured deme dynamics in the deterministic limit for well-mixed populations.
• Decreasing population density increases cooperator frequency until fixation.
• A critical population density exists below which cooperators abruptly disappear.
• Weak density fluctuations enhance cooperation, while strong fluctuations suppress it.

Conclusions:

• Cooperator-defector coexistence is robust in threshold public goods games, even in well-mixed populations.
• Population density is a critical factor influencing cooperation levels.
• Density fluctuations have a nuanced impact on cooperation, with weak fluctuations being beneficial and strong ones detrimental.