IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v15y2025i1d10.1007_s13235-024-00556-9.html
   My bibliography  Save this article

Group Selection Under the Replicator Dynamic

Author

Listed:
  • Ratul Lahkar

    (Ashoka University)

Abstract

We consider a society where individuals get divided into different groups. All groups play the same normal form game, and each group is in the basin of attraction of a particular strict Nash equilibrium of the game. Group selection refers to the evolution of the mass of each group under the replicator dynamic. We provide microfoundations to the replicator dynamic using revision protocols, wherein agents migrate between groups based on average payoffs of the groups. Individual selection of strategies within each group happens in two possible ways. Either all agents instantaneously coordinate on a strict Nash equilibrium or all agents change their strategies under the logit dynamic. In either case, the group playing the Pareto efficient Nash equilibrium gets selected. Individual selection under the logit dynamic may slow down the process and introduce non-monotonicity. We then apply the model to the stag hunt game.

Suggested Citation

  • Ratul Lahkar, 2025. "Group Selection Under the Replicator Dynamic," Dynamic Games and Applications, Springer, vol. 15(1), pages 129-153, March.
  • Handle: RePEc:spr:dyngam:v:15:y:2025:i:1:d:10.1007_s13235-024-00556-9
    DOI: 10.1007/s13235-024-00556-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-024-00556-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s13235-024-00556-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    3. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    4. Bandhu, Sarvesh & Lahkar, Ratul, 2023. "Survival of altruistic preferences in a large population public goods game," Economics Letters, Elsevier, vol. 226(C).
    5. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
    6. Hofbauer, Josef & Sandholm, William H., 2007. "Evolution in games with randomly disturbed payoffs," Journal of Economic Theory, Elsevier, vol. 132(1), pages 47-69, January.
    7. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    8. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    9. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    10. Bester, Helmut & Guth, Werner, 1998. "Is altruism evolutionarily stable?," Journal of Economic Behavior & Organization, Elsevier, vol. 34(2), pages 193-209, February.
    11. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    12. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    13. Lahkar, Ratul, 2019. "Elimination of non-individualistic preferences in large population aggregative games," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 150-165.
    14. Aviad Heifetz & Chris Shannon & Yossi Spiegel, 2007. "The Dynamic Evolution of Preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(2), pages 251-286, August.
    15. Lahkar, Ratul & Sandholm, William H., 2008. "The projection dynamic and the geometry of population games," Games and Economic Behavior, Elsevier, vol. 64(2), pages 565-590, November.
    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. William H. Sandholm & Mathias Staudigl, 2018. "Sample Path Large Deviations for Stochastic Evolutionary Game Dynamics," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1348-1377, November.
    2. Sarvesh Bandhu & Ratul Lahkar, 2023. "Evolutionary robustness of dominant strategy implementation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 685-721, August.
    3. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.
    4. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    5. Reinoud Joosten, 2009. "Paul Samuelson's critique and equilibrium concepts in evolutionary game theory," Papers on Economics and Evolution 2009-16, Philipps University Marburg, Department of Geography.
    6. Michael Kosfeld, 2002. "Stochastic strategy adjustment in coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(2), pages 321-339.
    7. Sandholm,W.H., 2003. "Excess payoff dynamics, potential dynamics, and stable games," Working papers 5, Wisconsin Madison - Social Systems.
    8. Mertikopoulos, Panayotis & Sandholm, William H., 2018. "Riemannian game dynamics," Journal of Economic Theory, Elsevier, vol. 177(C), pages 315-364.
    9. Edward Cartwright, 2002. "Learning to play approximate Nash equilibria in games with many players," Levine's Working Paper Archive 506439000000000070, David K. Levine.
    10. , & , H. & ,, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    11. Fudenberg, Drew & Imhof, Lorens A., 2006. "Imitation processes with small mutations," Journal of Economic Theory, Elsevier, vol. 131(1), pages 251-262, November.
    12. Sandholm, William H., 2015. "Population Games and Deterministic Evolutionary Dynamics," Handbook of Game Theory with Economic Applications,, Elsevier.
    13. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
    14. Weibull, Jörgen W., 1997. "What have we learned from Evolutionary Game Theory so far?," Working Paper Series 487, Research Institute of Industrial Economics, revised 26 Oct 1998.
    15. Gerard van der Laan & A.F. Tieman, 1996. "Evolutionary Game Theory and the Modelling of Economic Behavior," Tinbergen Institute Discussion Papers 96-172/8, Tinbergen Institute.
    16. Ratul Lahkar & Sayan Mukherjee & Souvik Roy, 2022. "A Deterministic Approximation Approach to the Continuum Logit Dynamic with an Application to Supermodular Games," Working Papers 79, Ashoka University, Department of Economics.
    17. Nicola Campigotto, 2021. "Pairwise imitation and evolution of the social contract," Journal of Evolutionary Economics, Springer, vol. 31(4), pages 1333-1354, September.
    18. Alós-Ferrer, Carlos & Weidenholzer, Simon, 2014. "Imitation and the role of information in overcoming coordination failures," Games and Economic Behavior, Elsevier, vol. 87(C), pages 397-411.
    19. Boyu Zhang & Josef Hofbauer, 2015. "Equilibrium selection via replicator dynamics in $$2 \times 2$$ 2 × 2 coordination games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 433-448, May.
    20. Apesteguia, Jose & Huck, Steffen & Oechssler, Jorg, 2007. "Imitation--theory and experimental evidence," Journal of Economic Theory, Elsevier, vol. 136(1), pages 217-235, September.

    More about this item

    Keywords

    Group selection; Replicator dynamic; Evolutionary game theory;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    Statistics

    Access and download statistics

    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:spr:dyngam:v:15:y:2025:i:1:d:10.1007_s13235-024-00556-9. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.