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Adaptive Dynamics of Extortion and Compliance

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  • Christian Hilbe
  • Martin A Nowak
  • Arne Traulsen

Abstract

Direct reciprocity is a mechanism for the evolution of cooperation. For the iterated prisoner’s dilemma, a new class of strategies has recently been described, the so-called zero-determinant strategies. Using such a strategy, a player can unilaterally enforce a linear relationship between his own payoff and the co-player’s payoff. In particular the player may act in such a way that it becomes optimal for the co-player to cooperate unconditionally. In this way, a player can manipulate and extort his co-player, thereby ensuring that the own payoff never falls below the co-player’s payoff. However, using a compliant strategy instead, a player can also ensure that his own payoff never exceeds the co-player’s payoff. Here, we use adaptive dynamics to study when evolution leads to extortion and when it leads to compliance. We find a remarkable cyclic dynamics: in sufficiently large populations, extortioners play a transient role, helping the population to move from selfish strategies to compliance. Compliant strategies, however, can be subverted by altruists, which in turn give rise to selfish strategies. Whether cooperative strategies are favored in the long run critically depends on the size of the population; we show that cooperation is most abundant in large populations, in which case average payoffs approach the social optimum. Our results are not restricted to the case of the prisoners dilemma, but can be extended to other social dilemmas, such as the snowdrift game. Iterated social dilemmas in large populations do not lead to the evolution of strategies that aim to dominate their co-player. Instead, generosity succeeds.

Suggested Citation

  • Christian Hilbe & Martin A Nowak & Arne Traulsen, 2013. "Adaptive Dynamics of Extortion and Compliance," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-9, November.
  • Handle: RePEc:plo:pone00:0077886
    DOI: 10.1371/journal.pone.0077886
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    References listed on IDEAS

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    Cited by:

    1. Masahiko Ueda & Toshiyuki Tanaka, 2020. "Linear algebraic structure of zero-determinant strategies in repeated games," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-13, April.
    2. Alexander J. Stewart & Joshua B. Plotkin, 2015. "The Evolvability of Cooperation under Local and Non-Local Mutations," Games, MDPI, vol. 6(3), pages 1-20, July.
    3. Yali Dong & Cong Li & Yi Tao & Boyu Zhang, 2015. "Evolution of Conformity in Social Dilemmas," PLOS ONE, Public Library of Science, vol. 10(9), pages 1-12, September.
    4. Kang, Kai & Tian, Jinyan & Zhang, Boyu, 2024. "Cooperation and control in asymmetric repeated games," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    5. Marc Harper & Vincent Knight & Martin Jones & Georgios Koutsovoulos & Nikoleta E Glynatsi & Owen Campbell, 2017. "Reinforcement learning produces dominant strategies for the Iterated Prisoner’s Dilemma," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-33, December.
    6. Christopher Lee & Marc Harper & Dashiell Fryer, 2015. "The Art of War: Beyond Memory-one Strategies in Population Games," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-16, March.
    7. Hilbe, Christian & Traulsen, Arne & Sigmund, Karl, 2015. "Partners or rivals? Strategies for the iterated prisoner's dilemma," Games and Economic Behavior, Elsevier, vol. 92(C), pages 41-52.
    8. Taha, Mohammad A. & Ghoneim, Ayman, 2021. "Zero-determinant strategies in infinitely repeated three-player prisoner's dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    9. Anton M Unakafov & Thomas Schultze & Alexander Gail & Sebastian Moeller & Igor Kagan & Stephan Eule & Fred Wolf, 2020. "Emergence and suppression of cooperation by action visibility in transparent games," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-32, January.
    10. Yohsuke Murase & Seung Ki Baek, 2021. "Friendly-rivalry solution to the iterated n-person public-goods game," PLOS Computational Biology, Public Library of Science, vol. 17(1), pages 1-17, January.
    11. Vincent Knight & Marc Harper & Nikoleta E Glynatsi & Owen Campbell, 2018. "Evolution reinforces cooperation with the emergence of self-recognition mechanisms: An empirical study of strategies in the Moran process for the iterated prisoner’s dilemma," PLOS ONE, Public Library of Science, vol. 13(10), pages 1-33, October.

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