Evolutionary dynamics of cooperation in a population with probabilistic corrupt enforcers and violators
Open accessAbstract
Pro-social punishment is a key driver of harmonious and stable society. However, this institution is vulnerable to corruption since law-violators can avoid sanctioning by paying bribes to corrupt law-enforcers. Consequently, to understand how altruistic behavior survives in a corrupt environment is an open question. To reveal potential explanations here, we introduce corrupt enforcers and violators into the public goods game with pool punishment, and assume that punishers, as corrupt enforcers, may select defectors probabilistically to take a bribe from, and meanwhile defectors, as corrupt violators, may select punishers stochastically to be corrupted. By means of mathematical analysis, we aim to study the necessary conditions for the evolution of cooperation in such corrupt environment. We find that cooperation can be maintained in the population in two distinct ways. First, cooperators, defectors, and punishers can coexist by all keeping a steady fraction of the population. Second, these three strategies can form a cyclic dominance that resembles a rock-scissors-paper cycle or a heteroclinic cycle. We theoretically identify conditions when the competing strategies coexist in a stationary way or they dominate each other in a cyclic way. These predictions are confirmed numerically.
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Altruistic punishment is ineffective when the possibility arises for punishing the cooperators.
“As far as altruistic punishment is concerned, it is ineffective when the possibility arises for punishing the cooperators, e.g., due to bribery42 or imperfect information43.”
From Cooperation without punishment (2023) · cites this paper as [42]
The Introduction (p. 2) says bribery can undermine punishment’s positive effect on cooperation. But the paper models defectors bribing enforcers to avoid punishment, not cooperators being punished; its Conclusions (p. 15) also say corruption can stabilize cooperation. It therefore does not support the claimed mechanism or an unqualified finding of ineffectiveness. (LLM, conf=0.82)
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References 68 · Cited by 128
Research works printed but not linked: 1
- [57]A. Traulsen, T. R¨ ohl, and M. Milinski, An economic experiment reveals that humans prefer pool punishment to maintain the commons, Proc. R. Soc. B 279 (2012) 3716-3721.
- Authors
- Liu, L., Chen, X., & Szolnoki, A.
- Affiliations
- University of Electronic Science and Technology of China (CN)
- Institute for Technical Physics and Materials Science (HU)
- Venue
- Mathematical Models and Methods in Applied Sciences
- Publisher
- World Scientific Pub Co Pte Ltd
- Published
- 2019-10
- Volume
- 29
- Issue
- 11
- Pages
- 2127-2149
- ISSN
- 0218-2025 (ISSN-L)
- 1793-6314
- OpenAlex
- W2966555906
- Cited by
- 128
- References
- 68
- Citations by year
- 2026: 15 · 2025: 22 · 2024: 19 · 2023: 18 · 2022: 20 · 2021: 18 · 2020: 15 · 2019: 1
- FWCI
- 27.19
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Mathematical Models and Methods in Applied Sciences (publishedVersion)
- Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) (acceptedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Natural Science Foundation of China (61976048, 61503062)
- Hungarian National Research Fund (K-120785)
- Topics
- Social Sciences › Sociology and Political Science › Evolutionary Game Theory and Cooperation
- Social Sciences › Safety Research › Experimental Behavioral Economics Studies
- Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
- Keywords
- evolution of cooperation, public goods game, corruption, bribery, stochastic selection, cyclic dominance, heteroclinic cycles, coexistence of strategies, altruism
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