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...阈值公共物品博弈（threshold public goods game）是最为经典的非线性公共物品困境模型之一。当假定种群遵循所谓的结构化局域种群（structured deme）模型时，合作者（cooperators）与背叛者（defectors）通常会在此博弈中稳定共存。本文构建了一类无局域种群结构的一般N人博弈动力学模型：个体与随机选取的邻居进行互动，选择过程发生在随机配对的个体之间。研究表明，在确定性极限条件下，该模型的动力学行为与结构化局域种群模型的复制子动力学（replicator dynamics）完全一致——即便是在种群完全均匀混合的场景下，阈值公共物品博弈中合作者与背叛者的共存仍是典型现象。本文进一步拓展模型，以探究密度依赖（density dependence）与密度波动（density fluctuation）对动力学过程的影响。通过解析与数值分析，我们发现降低种群密度会提升合作者的均衡频率，直至该策略完全固定……# 公共物品博弈中的合作无需分类结构，且依赖种群密度 https://doi.org/10.5061/dryad.pzgmsbcvm 本研究针对无局域种群结构的阈值公共物品博弈构建了动力学模型，并探究了密度依赖与密度波动的影响。 ## 文件说明 - `model1.py`：本文所述的与密度无关的基于智能体的模型（agent based model）的Python脚本。在此模型中，智能体分为合作者与背叛者两类，以群体为单位开展互动。系统会随机组建两个小组，组内成员进行博弈，并依据各自的收益确定替换概率。单个蒙特卡洛循环（Monte Carlo cycle）需重复该过程`group_size/2`次，等价于一次世代更新（generation update）。 - `model2.py`：本文所述的与密度相关的基于智能体的模型的Python脚本。相较于前述模型，该模型中个体将以概率`p_d`发生死亡……