- The evolution of cooperation in spatial public goods game with tolerant punishment based on reputation threshold

Snapshots of the spatial arrangements of strategies at four representative moments for different reputation thresholds. (a) R 0 = 0, (b) R 0 = 4, (c) R 0 = 12, and (d) R 0 = 16, and fixed enhancement factor r = 2.5 and b = 0.2. Each row from top to bottom represents a situation corresponding to a different reputation threshold R 0. Each column from left to right represents a different time step t. White pixels stand for cooperators and blue pixels for defectors. It is noteworthy that defectors can survive in an environment where no punishment is introduced ( R 0 = 0). However, in an environment with a higher reputation threshold ( R 0 = 4, 12, and 16), after 100 time steps, cooperators gradually gather to form stable clusters. Thus, a strict reputation evaluation environment can induce the formation and development of cooperator clusters.

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Reference

The evolution of cooperation in spatial public goods game with tolerant punishment based on reputation threshold - Scientific Figure on ResearchGate. Available from: https://www.researchgate.net/figure/Snapshots-of-the-spatial-arrangements-of-strategies-at-four-representative-moments-for_fig5_387704481 [accessed 24 Apr 2025]

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Snapshots of the spatial arrangements of strategies at four representative moments for different reputation thresholds. (a) R 0 = 0, (b) R 0 = 4, (c) R 0 = 12, and (d) R 0 = 16, and fixed enhancement factor r = 2.5 and b = 0.2. Each row from top to bottom represents a situation corresponding to a different reputation threshold R 0. Each column from left to right represents a different time step t. White pixels stand for cooperators and blue pixels for defectors. It is noteworthy that defectors can survive in an environment where no punishment is introduced ( R 0 = 0). However, in an environment with a higher reputation threshold ( R 0 = 4, 12, and 16), after 100 time steps, cooperators gradually gather to form stable clusters. Thus, a strict reputation evaluation environment can induce the formation and development of cooperator clusters.

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<a href="https://www.researchgate.net/figure/Snapshots-of-the-spatial-arrangements-of-strategies-at-four-representative-moments-for_fig5_387704481"><img src="https://www.researchgate.net/publication/387704481/figure/fig5/AS:11431281301266435@1735950939044/Snapshots-of-the-spatial-arrangements-of-strategies-at-four-representative-moments-for.jpg" alt="Snapshots of the spatial arrangements of strategies at four representative moments for different reputation thresholds. (a) R 0 = 0, (b) R 0 = 4, (c) R 0 = 12, and (d) R 0 = 16, and fixed enhancement factor r = 2.5 and b = 0.2. Each row from top to bottom represents a situation corresponding to a different reputation threshold R 0. Each column from left to right represents a different time step t. White pixels stand for cooperators and blue pixels for defectors. It is noteworthy that defectors can survive in an environment where no punishment is introduced ( R 0 = 0). However, in an environment with a higher reputation threshold ( R 0 = 4, 12, and 16), after 100 time steps, cooperators gradually gather to form stable clusters. Thus, a strict reputation evaluation environment can induce the formation and development of cooperator clusters."/></a>