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How to Analyze Models of Nonlinear Public Goods

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  • Marco Archetti

    (School of Biological Sciences, University of East Anglia, Norwich Research Park, Norwich NR4 7TJ, UK)

Abstract

Public goods games often assume that the effect of the public good is a linear function of the number of contributions. In many cases, however, especially in biology, public goods have nonlinear effects, and nonlinear games are known to have dynamics and equilibria that can differ dramatically from linear games. Here I explain how to analyze nonlinear public goods games using the properties of Bernstein polynomials, and how to approximate the equilibria. I use mainly examples from the evolutionary game theory of cancer, but the approach can be used for a wide range of nonlinear public goods games.

Suggested Citation

  • Marco Archetti, 2018. "How to Analyze Models of Nonlinear Public Goods," Games, MDPI, vol. 9(2), pages 1-15, April.
    • Handle: RePEc:gam:jgames:v:9:y:2018:i:2:p:17-:d:139503
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    References listed on IDEAS

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    1. Marco Archetti, 2014. "Stable Heterogeneity for the Production of Diffusible Factors in Cell Populations," PLOS ONE, Public Library of Science, vol. 9(9), pages 1-8, September.
    2. John Fox & Melvin Guyer, 1978. "“Public†Choice and Cooperation in n-Person Prisoner's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 22(3), pages 469-481, September.
    3. Jeff Gore & Hyun Youk & Alexander van Oudenaarden, 2009. "Snowdrift game dynamics and facultative cheating in yeast," Nature, Nature, vol. 459(7244), pages 253-256, May.
    4. Moritz Gerstung & Hani Nakhoul & Niko Beerenwinkel, 2011. "Evolutionary Games with Affine Fitness Functions: Applications to Cancer," Dynamic Games and Applications, Springer, vol. 1(3), pages 370-385, September.
    5. Javad Salimi Sartakhti & Mohammad Hossein Manshaei & Soroosh Bateni & Marco Archetti, 2016. "Evolutionary Dynamics of Tumor-Stroma Interactions in Multiple Myeloma," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-17, December.
    6. Jingsong Zhang & Jessica J. Cunningham & Joel S. Brown & Robert A. Gatenby, 2017. "Integrating evolutionary dynamics into treatment of metastatic castrate-resistant prostate cancer," Nature Communications, Nature, vol. 8(1), pages 1-9, December.
    7. D. Basanta & H. Hatzikirou & A. Deutsch, 2008. "Studying the emergence of invasiveness in tumours using game theory," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(3), pages 393-397, June.
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    Cited by:

    1. Nöldeke, Georg & Peña, Jorge, 2018. "Group size effects in social evolution," IAST Working Papers 18-75, Institute for Advanced Study in Toulouse (IAST).
    2. Matthijs van Veelen, 2020. "The evolution of morality," Tinbergen Institute Discussion Papers 20-063/I, Tinbergen Institute.
    3. Yang, Luhe & Zhang, Lianzhong, 2021. "Environmental feedback in spatial public goods game," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    4. Benjamin Wölfl & Hedy te Rietmole & Monica Salvioli & Artem Kaznatcheev & Frank Thuijsman & Joel S. Brown & Boudewijn Burgering & Kateřina Staňková, 2022. "The Contribution of Evolutionary Game Theory to Understanding and Treating Cancer," Dynamic Games and Applications, Springer, vol. 12(2), pages 313-342, June.
    5. Yang, Luhe & Zhang, Lianzhong & Yang, Duoxing, 2022. "Asymmetric micro-dynamics in spatial anonymous public goods game," Applied Mathematics and Computation, Elsevier, vol. 415(C).
    6. Javad Salimi Sartakhti & Mohammad Hossein Manshaei & Marco Archetti, 2018. "Game Theory of Tumor–Stroma Interactions in Multiple Myeloma: Effect of Nonlinear Benefits," Games, MDPI, vol. 9(2), pages 1-11, May.

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