IDEAS home Printed from https://ideas.repec.org/a/gam/jgames/v12y2021i4p72-d644428.html
   My bibliography  Save this article

Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach

Author

Listed:
  • Anuraag Bukkuri

    (Cancer Biology and Evolution Program and Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL 33612, USA)

  • Joel S. Brown

    (Cancer Biology and Evolution Program and Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, FL 33612, USA)

Abstract

Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating ( G ) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G -function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer.

Suggested Citation

  • Anuraag Bukkuri & Joel S. Brown, 2021. "Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach," Games, MDPI, vol. 12(4), pages 1-19, September.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:4:p:72-:d:644428
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2073-4336/12/4/72/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2073-4336/12/4/72/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bomze Immanuel M. & Weibull Jorgen W., 1995. "Does Neutral Stability Imply Lyapunov Stability?," Games and Economic Behavior, Elsevier, vol. 11(2), pages 173-192, November.
    2. B Suman & P Kumar, 2006. "A survey of simulated annealing as a tool for single and multiobjective optimization," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(10), pages 1143-1160, October.
    3. U. Dieckmann & R. Law, 1996. "The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes," Working Papers wp96001, International Institute for Applied Systems Analysis.
    4. Hernán Darío Toro-Zapata & Gerard Olivar-Tost & Fabio Dercole, 2018. "Conditions on the Energy Market Diversification from Adaptive Dynamics," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-15, September.
    5. Basu, Kaushik, 1990. "On the Non-existence of a Rationality Definition for Extensive Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 33-44.
    6. Basu, Kaushik, 1994. "The Traveler's Dilemma: Paradoxes of Rationality in Game Theory," American Economic Review, American Economic Association, vol. 84(2), pages 391-395, May.
    7. Khalil Amine, 2019. "Multiobjective Simulated Annealing: Principles and Algorithm Variants," Advances in Operations Research, Hindawi, vol. 2019, pages 1-13, May.
    8. Åke Brännström & Jacob Johansson & Niels Von Festenberg, 2013. "The Hitchhiker’s Guide to Adaptive Dynamics," Games, MDPI, vol. 4(3), pages 1-25, June.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Asma Khalil Alkhamis & Manar Hosny, 2023. "A Multi-Objective Simulated Annealing Local Search Algorithm in Memetic CENSGA: Application to Vaccination Allocation for Influenza," Sustainability, MDPI, vol. 15(21), pages 1-37, October.
    2. Velu, C. & Iyer, S., 2008. "The Rationality of Irrationality for Managers: Returns- Based Beliefs and the Traveller’s Dilemma," Cambridge Working Papers in Economics 0826, Faculty of Economics, University of Cambridge.
    3. Matthijs van Veelen & Benjamin Allen & Moshe Hoffman & Burton Simon & Carl Veller, 2016. "Inclusive Fitness," Tinbergen Institute Discussion Papers 16-055/I, Tinbergen Institute.
    4. Swami Iyer & Timothy Killingback, 2020. "Evolution of Cooperation in Social Dilemmas with Assortative Interactions," Games, MDPI, vol. 11(4), pages 1-31, September.
    5. Lindh, Magnus & Zhang, Lai & Falster, Daniel & Franklin, Oskar & Brännström, Åke, 2014. "Plant diversity and drought: The role of deep roots," Ecological Modelling, Elsevier, vol. 290(C), pages 85-93.
    6. Hernán Darío Toro-Zapata & Carlos Andrés Trujillo-Salazar & Fabio Dercole & Gerard Olivar-Tost, 2021. "Coffee Berry Borer (Hypothenemus hampei) and its role in the evolutionary diversification of the coffee market," Journal of Evolutionary Economics, Springer, vol. 31(3), pages 1029-1063, July.
    7. Nassar, Elma & Pardoux, Etienne, 2019. "Small jumps asymptotic of the moving optimum Poissonian SDE," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2320-2340.
    8. Ispano, Alessandro & Schwardmann, Peter, 2017. "Cooperating over losses and competing over gains: A social dilemma experiment," Games and Economic Behavior, Elsevier, vol. 105(C), pages 329-348.
    9. Yuval Heller & Eyal Winter, 2020. "Biased-Belief Equilibrium," American Economic Journal: Microeconomics, American Economic Association, vol. 12(2), pages 1-40, May.
    10. Van Damme, Eric, 2002. "Strategic equilibrium," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 41, pages 1521-1596, Elsevier.
    11. Joëlle Noailly, 2008. "Coevolution of economic and ecological systems," Journal of Evolutionary Economics, Springer, vol. 18(1), pages 1-29, February.
    12. Gisèle Umbhauer, 2019. "Traveler’s dilemma : how the value of the luggage influences behavior," Working Papers of BETA 2019-13, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    13. van Damme, E.E.C., 1995. "Game theory : The next stage," Other publications TiSEM 7779b0f9-bef5-45c7-ae6b-7, Tilburg University, School of Economics and Management.
    14. Chen, Daniel L. & Schonger, Martin & Wickens, Chris, 2016. "oTree—An open-source platform for laboratory, online, and field experiments," Journal of Behavioral and Experimental Finance, Elsevier, vol. 9(C), pages 88-97.
    15. Leonardo Becchetti & Emanuele Bobbio & Federico Prizia & Lorenzo Semplici, 2022. "Going Deeper into the S of ESG: A Relational Approach to the Definition of Social Responsibility," Sustainability, MDPI, vol. 14(15), pages 1-22, August.
    16. Asheim, G.B. & Dufwenberg, M., 1996. "Admissibility and Common Knowledge," Discussion Paper 1996-16, Tilburg University, Center for Economic Research.
    17. Aradhana Narang & A. J. Shaiju, 2019. "Evolutionary Stability of Polymorphic Profiles in Asymmetric Games," Dynamic Games and Applications, Springer, vol. 9(4), pages 1126-1142, December.
    18. Felipe, Ángel & Ortuño, M. Teresa & Righini, Giovanni & Tirado, Gregorio, 2014. "A heuristic approach for the green vehicle routing problem with multiple technologies and partial recharges," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 111-128.
    19. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    20. Jacob K. Goeree & Charles A. Holt, 2001. "Ten Little Treasures of Game Theory and Ten Intuitive Contradictions," American Economic Review, American Economic Association, vol. 91(5), pages 1402-1422, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jgames:v:12:y:2021:i:4:p:72-:d:644428. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.