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

The threshold public goods game is one of the best-known models of nonlinear public goods dilemmas. Cooperators and defectors typically coexist in this game when the population is assumed to follow the so-called structured deme model. In this paper we develop a dynamical model of a general N-player game in which there is no deme structure: individuals interact with randomly chosen neighbours and selection occurs between randomly chosen pairs of indi- viduals. We show that in the deterministic limit the dynamics in this model leads to the same replicator dynamics as in the structured deme model, i.e. coexistence of cooperators and defectors is typical in threshold public goods game even when the population is completely well-mixed. We extend the model to study the effect of density dependence and density fluctuation on the dynamics. We show analytically and numerically that decreasing population density increases the equilibrium frequency of cooperators till the fixation of this strategy, b..., , , # Cooperation in public goods game does not require assortment and depends on population density

[https://doi.org/10.5061/dryad.pzgmsbcvm](https://doi.org/10.5061/dryad.pzgmsbcvm)

The study introduces a dynamical model for the threshold public goods game without deme structure and explores the impact of density dependence and fluctuations.

## Description of the files

Files:

model1.py: Python script of the density independent agent based model that is described in the paper

In this model, agents, either cooperators or defectors, interact in groups. Two groups are randomly formed, and individuals within them play a game, determining replacement probabilities based on their payoffs. This process repeats group_size/2 times for a single Monte Carlo cycle, equivalent to one generation update.

model2.py: Python script of the density dependent agent based model that is described in the paper

In this model in addition to the previous one, individuals may die with a probability of p_d, t...