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The Price Identity of Replicator(–Mutator) Dynamics on Graphs with Quantum Strategies in a Public Goods Game

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  • Arnaud Z. Dragicevic

    (CIRANO — Centre Interuniversitaire de Recherche en Analyse des Organisations
    Chulalongkorn University)

Abstract

Our research explores the influence of quantum strategies on the Price identity of replicator(–mutator) dynamics in networked systems. We specifically focus on potential solutions to social dilemmas through a quantum interpretation of the public goods game. The outcomes of our investigation defy the expected simplicity, suggesting that quantum strategies do not invariably induce cooperative behavior. Within the framework of replicator dynamics, based on a stratified interaction mechanism and a composite strategy update rule, complete entanglement could lead to super-cooperators dominating, given the cooperation and defection probabilities exceed zero. In replicator–mutator dynamics, super-cooperators reach their peak density when mutation leaning toward cooperation is certain. Numerical simulations corroborate our theoretical propositions, shedding light on the roles of various subpopulations as either complementary or substitutive entities. Our research underscores how quantum strategies accentuate observed patterns compared to non-entangled scenarios, and how the assuredness of mutation markedly impacts the behavior of super-cooperators.

Suggested Citation

  • Arnaud Z. Dragicevic, 2025. "The Price Identity of Replicator(–Mutator) Dynamics on Graphs with Quantum Strategies in a Public Goods Game," Dynamic Games and Applications, Springer, vol. 15(1), pages 74-102, March.
    • Handle: RePEc:spr:dyngam:v:15:y:2025:i:1:d:10.1007_s13235-024-00560-z
    DOI: 10.1007/s13235-024-00560-z
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    References listed on IDEAS

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    1. Calford, Evan M., 2020. "Uncertainty aversion in game theory: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 176(C), pages 720-734.
    2. Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
    3. Francisco C. Santos & Marta D. Santos & Jorge M. Pacheco, 2008. "Social diversity promotes the emergence of cooperation in public goods games," Nature, Nature, vol. 454(7201), pages 213-216, July.
    4. Qi Su & Lei Zhou & Long Wang, 2019. "Evolutionary multiplayer games on graphs with edge diversity," PLOS Computational Biology, Public Library of Science, vol. 15(4), pages 1-22, April.
    5. Arnaud Z. Dragicevic, 2016. "From robustness to resilience: A network Price identity approach," Post-Print hal-01493080, HAL.
    6. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    7. Martin A. Nowak & Karl Sigmund, 1998. "Evolution of indirect reciprocity by image scoring," Nature, Nature, vol. 393(6685), pages 573-577, June.
    8. Li, Qiang & Iqbal, Azhar & Chen, Minyou & Abbott, Derek, 2012. "Quantum strategies win in a defector-dominated population," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3316-3322.
    9. M.A. Nowak & K. Sigmund, 1998. "Evolution of Indirect Reciprocity by Image Scoring/ The Dynamics of Indirect Reciprocity," Working Papers ir98040, International Institute for Applied Systems Analysis.
    10. Angsheng Li & Xi Yong, 2015. "Emergence of Super Cooperation of Prisoner’s Dilemma Games on Scale-Free Networks," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-24, February.
    11. Martin A. Nowak & Karl Sigmund & Martin L. Leibowitz, 2000. "Cooperation versus Competition," Financial Analysts Journal, Taylor & Francis Journals, vol. 56(4), pages 13-22, July.
    12. Benjamin Allen & Gabor Lippner & Yu-Ting Chen & Babak Fotouhi & Naghmeh Momeni & Shing-Tung Yau & Martin A. Nowak, 2017. "Evolutionary dynamics on any population structure," Nature, Nature, vol. 544(7649), pages 227-230, April.
    13. Brandenburger, Adam, 2010. "The relationship between quantum and classical correlation in games," Games and Economic Behavior, Elsevier, vol. 69(1), pages 175-183, May.
    14. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    15. Arnaud Z. Dragicevic, 2017. "Option Fund Market Dynamics for Threshold Public Goods," Dynamic Games and Applications, Springer, vol. 7(1), pages 21-33, March.
    16. Alex McAvoy & Benjamin Allen & Martin A. Nowak, 2020. "Social goods dilemmas in heterogeneous societies," Nature Human Behaviour, Nature, vol. 4(8), pages 819-831, August.
    17. D. Timothy Bishop & Mark Broom & Richard Southwell, 2020. "Chris Cannings: A Life in Games," Dynamic Games and Applications, Springer, vol. 10(3), pages 591-617, September.
    18. Qi Su & Alex McAvoy & Yoichiro Mori & Joshua B. Plotkin, 2022. "Evolution of prosocial behaviours in multilayer populations," Nature Human Behaviour, Nature, vol. 6(3), pages 338-348, March.
    19. Vassili N. Kolokoltsov, 2022. "Dynamic Quantum Games," Dynamic Games and Applications, Springer, vol. 12(2), pages 552-573, June.
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