Note
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Public goods game on a hypergraph
Every hyperedge of a random hypergraph is a group that plays the public goods game. A cooperator pays 1 in each of its groups, the pot is multiplied by the synergy and shared by the members, and every player copies a random neighbour with the Fermi probability of their payoffs. Cooperation needs a synergy near the sizes of the hyperedges.
Four hundred players form hyperedges of sizes 3 and 5, half of them start as cooperators, and the synergy is 4. The default blueprint shows the strategies on the network.
import matplotlib.pyplot as plt
import numpy as np
from skcomplex.engine.runtime import Simulation
from skcomplex.engine.viz import RerunObserver
from skcomplex.models import create
MODEL = 'hypergraph_public_goods'
ROUNDS = 100
observer = RerunObserver(MODEL, save_path=f'{MODEL}.rrd', blueprint='default', interval=1)
system = create(MODEL)
simulation = Simulation(system, observers=[observer], random_state=0).check().prepare().run(until=ROUNDS)
Open the recording in the Rerun viewer
Cooperation against the synergy
In a well-mixed population defection wins in a group of m for a synergy below m. The share of cooperators at the
end of runs should rise with the synergy across the sizes of the hyperedges.
def cooperators(synergy):
"""Return the share of cooperators at the end of a run."""
run = Simulation(create(MODEL, synergy=synergy), random_state=0).check().prepare().run(until=ROUNDS)
return np.asarray(run.trajectory_.values('players.strategy'))[-1].mean()
synergies = np.linspace(1.0, 7.0, 7)
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(synergies, [cooperators(synergy) for synergy in synergies], 'o-')
ax.set_xlabel('synergy')
ax.set_ylabel(f'share of cooperators after {ROUNDS} rounds')
ax.set_title('Synergy sustains cooperation on a hypergraph')
plt.show()
About the model
The public goods game on a hypergraph, played in every hyperedge, with Fermi imitation.
References
- Alvarez-Rodriguez et al. 2021
- Majhi et al. 2022
Total running time of the script: ( 0 minutes 3.366 seconds)
Download Python source code: plot_hypergraph_public_goods.py
Download Jupyter notebook: plot_hypergraph_public_goods.ipynb