Spatial-PGGs-any-network

This includes a Matlab function for calculating the critical synergy factor of spatial PGGs on any network structure and Python programs for agent-based simulations.

Files

• everythingrbcaccu.m - A matlab function. Please input population size N and $N\times N$ adjacency matrix wij.

If wij(i,j)=1 then i and j are neighbors, and vice versa if wij(i,j)=0.

The function will then return [rPC,rDB,rBD,rPCaccu,rDBaccu,rBDaccu,bcPC,bcDB,bcBD,bcPCaccu,bcDBaccu,bcBDaccu]. "r" means critical synergy factor in spatial PGGs. "bc" means critical benefit-to-cost ratio in spatial DGs. "PC" "DB" "BD" means the three update rules. "accu" means accumulated payoff (if there is no "accu" then it is averaged payoff).

• demo.m - A demonstration for the use of everythingrbc_accu.m, taking the star graph as an example.

• pgggraph_PC.py - A python program for agent-based simulations of spatial PGGs using averaged payoffs under the PC rule.

• pgggraph_DB.py - A python program for agent-based simulations of spatial PGGs using averaged payoffs under the DB rule.

System requirements

• We use Matlab 2022a and Python 3.9 in PyCharm.

• We used the mentioned softwares in Windows 11.

Installation guide

• Simply download Matlab and PyCharm in their official websites. Matlab may need costly subscription.

• Install the required packages within these softwares if there is any error report.

• Typical install time may be within one hour.

Demo of Matlab

• For numerical solutions of the theoretical predictions on specific networks, refer to demo.m.
• It shows an example of the $n=9$ star graph.
• Please put demo.m and everythingrbc_accu.m in the same fold and run demo.m.
• The outcome should be the critical synergy factors for cooperation success in spatial PGGs (and critical benefit-to-cost ratio in DGs) across all model details.
• Typical run time should be within 2 seconds.

Demo of Python

• For agent-based simulations on star graphs, refer to pgggraphPC.py and pgggraphDB.py, depending on the update rule you need.
• You may need to create a project in Python, with a "main.py" file. You can add pgggraphPC.py and pgggraphDB.py into your project and run them.
• The outcome should be the average stationary cooperation fraction as a function of synergy factor $r$.
• Typical run time should be more than 24 hours, depending on the performance of your computer. This is a parallel program and may take up all of your computer's CPU resources.

Q&A

For any question about this program, please contact

Chaoqian Wang, Email: CqWang814921147@outlook.com