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The leading eight:�Social norms that can maintain cooperation by indirect reciprocity

Hisashi Ohtsuki and Yoh Iwasa

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Journal of Theoretical Biology 239 (2006) 435-444

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Indirect reciprocity

  • Reputations: Good (G) or Bad (B)

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  • Actions: Cooperation ( ) or Defection ( )

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  • A large population

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    • Two players are randomly picked.�(player 1: focal player, player 2: opponent)

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    • They cooperate or defect each other simultaneously by using their own “behavioral strategy”.

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    • They change their partner.

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Indirect reciprocity

  • 4 possible reputation pairs and��2 possible actions for each given reputation pair

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    • 16 different behavioral strategies

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    • 256 different reputation dynamics

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Indirect reciprocity

  • 16 X 256 = 4096 different social norms
  • 4 possible reputation pairs and��2 possible actions for each given reputation pair

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    • 16 different behavioral strategies

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    • 256 different reputation dynamics

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Evolutionarily Stable Strategies (ESSs)�with high cooperation level

 

  • Repeat the above process for all possible norms

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The leading eight

C. Hilbe et al., vol. 115, no. 48, PNAS (2018)

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The leading eight

Characteristics of the leading eight

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  1. Maintenance of cooperation

C. Hilbe et al., vol. 115, no. 48, PNAS (2018)

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The leading eight

Characteristics of the leading eight

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  1. Maintenance of cooperation

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  • Identification of defectors

C. Hilbe et al., vol. 115, no. 48, PNAS (2018)

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The leading eight

Characteristics of the leading eight

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  1. Maintenance of cooperation

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  • Identification of defectors

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  • Punishment and justification of punishment

C. Hilbe et al., vol. 115, no. 48, PNAS (2018)

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The leading eight

Characteristics of the leading eight

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  1. Maintenance of cooperation

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  • Identification of defectors

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  • Punishment and justification of punishment

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  • Apology and forgiveness

C. Hilbe et al., vol. 115, no. 48, PNAS (2018)

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Summary

Cooperation is maintained in the population composed of that type only.

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When cheaters invade, they should be detected and labeled immediately.

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Those who are labeled as “bad” are refused cooperation by other members of the population, while those who refused help to them are regarded as good.

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The player who got a bad reputation by occasional unavoidable errors should apologize, and he will be forgiven and can return to the good reputation again.