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Where Do Mistakes Lead? A Survey of Games with Incompetent Players

Author

Listed:
  • Thomas Graham

    (University of Queensland)

  • Maria Kleshnina

    (Institute of Science and Technology Austria (IST Austria)
    Institute for Advanced Studies in Toulouse)

  • Jerzy A. Filar

    (University of Queensland)

Abstract

Mathematical models often aim to describe a complicated mechanism in a cohesive and simple manner. However, reaching perfect balance between being simple enough or overly simplistic is a challenging task. Frequently, game-theoretic models have an underlying assumption that players, whenever they choose to execute a specific action, do so perfectly. In fact, it is rare that action execution perfectly coincides with intentions of individuals, giving rise to behavioural mistakes. The concept of incompetence of players was suggested to address this issue in game-theoretic settings. Under the assumption of incompetence, players have non-zero probabilities of executing a different strategy from the one they chose, leading to stochastic outcomes of the interactions. In this article, we survey results related to the concept of incompetence in classic as well as evolutionary game theory and provide several new results. We also suggest future extensions of the model and argue why it is important to take into account behavioural mistakes when analysing interactions among players in both economic and biological settings.

Suggested Citation

  • Thomas Graham & Maria Kleshnina & Jerzy A. Filar, 2023. "Where Do Mistakes Lead? A Survey of Games with Incompetent Players," Dynamic Games and Applications, Springer, vol. 13(1), pages 231-264, March.
    • Handle: RePEc:spr:dyngam:v:13:y:2023:i:1:d:10.1007_s13235-022-00425-3
    DOI: 10.1007/s13235-022-00425-3
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    References listed on IDEAS

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    1. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
    2. Fudenberg, D. & Harris, C., 1992. "Evolutionary dynamics with aggregate shocks," Journal of Economic Theory, Elsevier, vol. 57(2), pages 420-441, August.
    3. Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    4. repec:nas:journl:v:115:y:2018:p:12241-12246 is not listed on IDEAS
    5. Bomze Immanuel M. & Burger Reinhard, 1995. "Stability by Mutation in Evolutionary Games," Games and Economic Behavior, Elsevier, vol. 11(2), pages 146-172, November.
    6. Fabio Dercole & Sergio Rinaldi, 2008. "Introduction to Analysis of Evolutionary Processes: The Adaptive Dynamics Approach and Its Applications," Introductory Chapters, in: Analysis of Evolutionary Processes: The Adaptive Dynamics Approach and Its Applications, Princeton University Press.
    7. Maria Kleshnina & Sabrina S. Streipert & Jerzy A. Filar & Krishnendu Chatterjee, 2020. "Prioritised Learning in Snowdrift-Type Games," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    8. Konstantin Avrachenkov & Vivek S. Borkar, 2019. "Metastability in Stochastic Replicator Dynamics," Dynamic Games and Applications, Springer, vol. 9(2), pages 366-390, June.
    9. Frey, Erwin, 2010. "Evolutionary game theory: Theoretical concepts and applications to microbial communities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(20), pages 4265-4298.
    10. 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.
    11. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    12. Andrew R. Tilman & Joshua B. Plotkin & Erol Akçay, 2020. "Evolutionary games with environmental feedbacks," Nature Communications, Nature, vol. 11(1), pages 1-11, December.
    13. Maria Kleshnina & Sabrina S Streipert & Jerzy A Filar & Krishnendu Chatterjee, 2021. "Mistakes can stabilise the dynamics of rock-paper-scissors games," PLOS Computational Biology, Public Library of Science, vol. 17(4), pages 1-16, April.
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