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The evolution of cooperation and punishment in spatial public goods games with bribery

Author

Listed:
  • Ding, Rui
  • Wang, Xianjia
  • Quan, Ji
  • Ma, Shuting
  • Zhao, Jinhua

Abstract

Altruistic punishment provides a compelling explanation for the prevalence of cooperation in social dilemmas. However, defectors often have an incentive to bribe punishers to avoid sanctions, while punishers may accept bribes and save punishment costs. To explore the impact of bribe on cooperation in structured populations, we introduce bribers and bribees into the spatial public goods game with punishment. By studying the phase transitions of this five-strategy system, we aim to uncover the underlying mechanisms behind strategy competition. Our findings reveal that bribers collude with bribees to invade other strategies, both directly at multi-strategy interface and indirectly through mediators such as defectors or bribers. Consequently, bribers protect bribe-recipients from invasion by defectors, leading to increased contribution levels when punishment intensity is relatively weak. However, when the fine is sufficiently high to empower punishers in confront defectors effectively, bribe can undermine the maintenance of punishment. Interestingly, the competitive advantage of bribers and bribe-recipients diminishes as bribery funds increase, leading to the emergence of a cyclic state involving three strategies: bribers, bribe-recipients and defectors.

Suggested Citation

  • Ding, Rui & Wang, Xianjia & Quan, Ji & Ma, Shuting & Zhao, Jinhua, 2025. "The evolution of cooperation and punishment in spatial public goods games with bribery," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
    • Handle: RePEc:eee:chsofr:v:193:y:2025:i:c:s0960077925001481
    DOI: 10.1016/j.chaos.2025.116135
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