Understand the game model of public goods, the evolution and dissemination of cooperation, and the impact of rewards and punishments on cooperation evolution under random networks, and use Monte Carlo simulation analysis to achieve mechanism modeling.
There are many restaurants of all sizes in the city, and each restaurant has a probability of being subjected to hygiene checks by relevant departments every day. If hygiene is not done on that day (i.e. betrayal), fines will be imposed. Use this mechanism to demonstrate cooperation and betrayal on four networks.
When an individual is a collaborator and regardless of whether they undergo inspection or not, the collaborator has already done a good job of hygiene and will not be punished. At this point, the profit that the individual collaborator obtains from the whole is as follows:
When an individual is a betrayer and the probability of being tested meets the following criteria.
The betrayer has not yet done a good job in hygiene, and at this point, the benefits of the betrayer are:
Rewards are awarded when the group cooperation rate is less than 0.5. Finally, calculate the total income of the individual:
Plus benefits from other groups
Parameter Description:
c: Cooperation costs for collaborators
r: Input-output ratio
k: Rationality level
penaltyAmount: Fine
rewardAmount: Reward
reward: group reward
Cooperation_rate: Group combination work rate
M1: Number of rows
M2: Number of columns
N: Number of game rounds
A: Denotes a collaborator or betrayer
D: Benefits of each individual in the group
E: Total income per individual
tongji: stores the proportion of collaborators at each moment
NC: represents the number of co authors in group i
NCD: Number of individuals in group i
totalpay: Represented as the total return of individual i playing games in multiple groups
individualRewards: All rewards received by individuals
| Network Type | Default (penalty=1, reward=7) |
Higher Penalty (penalty=3, reward=7) |
Higher Reward (penalty=1, reward=12) |
|---|---|---|---|
| BA scale-free |  |
 |
 |
| Random |  |
 |
 |
| Regular lattice |  |
 |
 |
| Small-world |  |
 |
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The three columns compare the evolution of the cooperation ratio under different parameters: default as baseline, higher penalty shows the suppression effect of increased fines on betrayal, and higher reward shows the promotion effect of increased rewards on cooperation. The four network structures (BA scale-free, random, regular lattice, small-world) are arranged top to bottom for cross-comparison of how network topology affects cooperation evolution.
The 12 evolution curves under .img/ are generated following the steps below. Both MATLAB and GNU Octave are supported — see platform-specific notes below.
Octave users: Octave requires the
statisticspackage for therandifunction. Load it first:pkg load statistics
Run one of the four network scripts to create the Node_neighbor adjacency matrix in the workspace. These scripts work identically in MATLAB and Octave:
% Pick one network (example: BA scale-free):
run('scaleFreeNetwork.m') % BA scale-free network
% run('randomNetwork.m') % Random network
% run('reluNetwork.m') % Regular lattice network
% run('smallWorldNetwork.m') % Small-world networkgoodGame.m uses the Node_neighbor matrix to run a Monte Carlo simulation (3500 rounds by default) and plots the cooperation ratio over time.
MATLAB users: Simply use run as shown below.
Octave users: goodGame.m is compatible with Octave. If the figure window does not appear, add figure; at the top of the script, or run graphics_toolkit('qt') in Octave first to switch the rendering backend.
Modify the parameters at the top of goodGame.m, then run and save the figure. Example for the BA scale-free network:
| Figure | Parameter Change | Output File |
|---|---|---|
| Default baseline | No change (penaltyAmount=1, rewardAmount=7) |
.img/BAnetwork.png |
| Higher penalty | Change line 4 to penaltyAmount=3 |
.img/BAnetworkpenaltyAmount.png |
| Higher reward | Restore line 4 to 1, change line 5 to rewardAmount=12 |
.img/BAnetworkrewardAmount.png |
% ---- 1st figure: default parameters ----
run('scaleFreeNetwork.m') % generate network
% goodGame.m params at default: penaltyAmount=1, rewardAmount=7
run('goodGame.m')
% In the figure window: File → Save As → .img/BAnetwork.png
% Or via command:
% MATLAB: saveas(gcf, '.img/BAnetwork.png')
% Octave: print('-dpng', '.img/BAnetwork.png')
% ---- 2nd figure: higher penalty ----
% Change goodGame.m line 4 to: penaltyAmount=3
run('goodGame.m')
saveas(gcf, '.img/BAnetworkpenaltyAmount.png')
% ---- 3rd figure: higher reward ----
% Restore goodGame.m line 4 to 1, change line 5 to: rewardAmount=12
run('goodGame.m')
saveas(gcf, '.img/BAnetworkrewardAmount.png')Octave save command (slightly different from MATLAB):
print('-dpng', '-r120', '.img/BAnetwork.png') % -r120 sets output resolutionRepeat steps 1-3 for each network type to produce all 12 figures:
.img/BAnetwork.png .img/BAnetworkpenaltyAmount.png .img/BAnetworkrewardAmount.png
.img/randomnetwork.png .img/randomnetworkpenaltyAmount.png .img/randomnetworkrewardAmount.png
.img/rulenetwork.png .img/rulenetworkpenaltyAmount.png .img/rulenetworkrewardAmount.png
.img/smallworldnetwork.png .img/smallworldnetworkpenaltyAmount.png .img/smallworldnetworkrewardAmount=7.png
Line 85 of goodGame.m controls the plot color and line style:
plot(1:length(tongji), tongji, '-r', 'LineWidth', 0.5)
% ^^^
% '-r' = red solid '-b' = blue solid '-g' = green solid
% '--r' = red dashed '-.b' = blue dash-dot ':k' = black dottedCombined with hold on on line 89, you can overlay multiple curves with different colors on the same figure for comparison.
This project uses Matlab Git. Go check them out if you don't have them locally installed.
$ git clone https://github.com/touero/silver-carp.gitFeel free to dive in! Open an issue or submit PRs.
This project exists thanks to all the people who contribute.