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Two-layer network model of public goods games with intervention and corruption
Zhenyu Shi1, Wei Wei1, Baifeng Li1
1School of Mathematical Sciences, Beihang University, Beijing 100191, China.
Chaos (Woodbury, N.Y.)
|July 1, 2022
Summary
Even corrupt umpires improve social efficiency in public goods games. Cooperation is influenced by umpire fairness, system development, and spatial distribution, with bribe costs determining full cooperation.
Area of Science:
- Social Dilemmas
- Game Theory
- Network Science
Background:
- Public goods games model social dilemmas where individual rationality conflicts with collective benefit.
- Cooperative behavior emerges despite defection being the individually rational choice.
- Punishment mechanisms promote cooperation but depend on fair third-party enforcement.
Purpose of the Study:
- To investigate the impact of umpire corruption on punishment mechanisms in public goods games.
- To analyze how factors like umpire fairness, spatial distribution, and costs influence cooperation.
- To model these interactions within a multilayer network framework.
Main Methods:
- Development of an umpire intervention model incorporating corruption within a multilayer network.
- Simulation of public goods games with fair and corrupt umpires.
- Analysis of Monte Carlo simulation results varying umpire fraction (ρ), spatial distribution, fine cost (α), and bribe cost (β).
Main Results:
- Umpire intervention consistently enhances social efficiency, irrespective of corruption levels.
- System development positively correlates with resistance to corruption.
- Spatial distribution (staggered vs. centralized) has opposing effects on cooperation, contingent on ρ and r.
- Full occupation of cooperators depends solely on the bribe cost (β) exceeding a specific threshold.
Conclusions:
- Corruption's impact on cooperation is nuanced, with intervention always beneficial for social efficiency.
- System architecture and economic parameters (fine/bribe costs) critically shape cooperative outcomes.
- The model provides insights into maintaining cooperation in social dilemmas with imperfect enforcement.
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