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Reactive means in the iterated Prisoner’s dilemma

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  • Molnar, Grant
  • Hammond, Caroline
  • Fu, Feng

Abstract

The Iterated Prisoner’s Dilemma (IPD) is a well studied framework for understanding direct reciprocity and cooperation in pairwise encounters. However, measuring the morality of various IPD strategies is still largely lacking. Here, we partially address this issue by proposing a suit of plausible morality metrics to quantify four aspects of justice. We focus our closed-form calculation on the class of reactive strategies because of their mathematical tractability and expressive power. We define reactive means as a tool for studying how actors in the IPD and Iterated Snowdrift Game (ISG) behave under typical circumstances. We compute reactive means for four functions intended to capture human intuitions about “goodness” and “fair play”. Two of these functions are strongly anticorrelated with success in the IPD and ISG, and the other two are weakly anticorrelated with success. Our results will aid in evaluating and comparing powerful IPD strategies based on machine learning algorithms, using simple and intuitive morality metrics.

Suggested Citation

  • Molnar, Grant & Hammond, Caroline & Fu, Feng, 2023. "Reactive means in the iterated Prisoner’s dilemma," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    • Handle: RePEc:eee:apmaco:v:458:y:2023:i:c:s0096300323003703
    DOI: 10.1016/j.amc.2023.128201
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    References listed on IDEAS

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    1. Christian Hilbe & Krishnendu Chatterjee & Martin A. Nowak, 2018. "Publisher Correction: Partners and rivals in direct reciprocity," Nature Human Behaviour, Nature, vol. 2(7), pages 523-523, July.
    2. Christian Hilbe & Krishnendu Chatterjee & Martin A. Nowak, 2018. "Partners and rivals in direct reciprocity," Nature Human Behaviour, Nature, vol. 2(7), pages 469-477, July.
    3. Takahiro Ezaki & Yutaka Horita & Masanori Takezawa & Naoki Masuda, 2016. "Reinforcement Learning Explains Conditional Cooperation and Its Moody Cousin," PLOS Computational Biology, Public Library of Science, vol. 12(7), pages 1-13, July.
    4. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    5. Ethan Akin, 2015. "What You Gotta Know to Play Good in the Iterated Prisoner’s Dilemma," Games, MDPI, vol. 6(3), pages 1-16, June.
    6. Jelena Grujić & Constanza Fosco & Lourdes Araujo & José A Cuesta & Angel Sánchez, 2010. "Social Experiments in the Mesoscale: Humans Playing a Spatial Prisoner's Dilemma," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-9, November.
    7. Wang, Shengxian & Chen, Xiaojie & Xiao, Zhilong & Szolnoki, Attila, 2022. "Decentralized incentives for general well-being in networked public goods game," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    8. İzgi, Burhaneddin & Özkaya, Murat & Üre, Nazım Kemal & Perc, Matjaž, 2023. "Extended matrix norm method: Applications to bimatrix games and convergence results," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    9. 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.
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