IDEAS home Printed from https://ideas.repec.org/p/bir/birmec/13-05.html
   My bibliography  Save this paper

Evolutionary Games with Group Selection

Author

Listed:
  • Martin Kaae Jensen
  • Alexandros Rigos

Abstract

This paper introduces two new concepts in evolutionary game theory; Nash equilibrium with Group Selection (NEGS) and Evolutionary Stable Strategy with Group Selection (ESSGS). These concepts generalize Maynard Smith and Price (1973) to settings with arbitrary matching rules, in particular they reduce, respectively, to Nash equilibrium and ESS when matching is random. NEGS are ESSGS are to the canonical group selection model of evolutionary theory what Nash Equilibrium and ESS are the standard replicator dynamics: any NEGS is a steady state, any stable steady state is a NEGS, and any ESSGS is asymptotically stable. We exploit this to prove what may be called "the second welfare theorem of evolution": Any evolutionary optimum will be a BEGS under some matching rule. Our results are illustrated in Hawk-Dove, Prisoners' dilemma, and Stage Hunt games.

Suggested Citation

  • Martin Kaae Jensen & Alexandros Rigos, 2012. "Evolutionary Games with Group Selection," Discussion Papers 13-05, Department of Economics, University of Birmingham.
    • Handle: RePEc:bir:birmec:13-05
    as

    Download full text from publisher

    File URL: https://repec.cal.bham.ac.uk/pdf/13-05.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    3. Larry Samuelson, 2002. "Evolution and Game Theory," Journal of Economic Perspectives, American Economic Association, vol. 16(2), pages 47-66, Spring.
    4. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    5. Ingela Alger & Jörgen W. Weibull, 2010. "Kinship, Incentives, and Evolution," American Economic Review, American Economic Association, vol. 100(4), pages 1725-1758, September.
    6. Carlsson, H. & van Damme, E.E.C., 1990. "Global games and equilibrium selection," Other publications TiSEM 698f4897-46c6-4097-8265-2, Tilburg University, School of Economics and Management.
    7. Rubinstein, Ariel, 1979. "Equilibrium in supergames with the overtaking criterion," Journal of Economic Theory, Elsevier, vol. 21(1), pages 1-9, August.
    8. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
    9. Ilan Eshel & Larry Samuelson & Avner Shaked, "undated". "Altruists Egoists and Hooligans in a Local Interaction Model," ELSE working papers 005, ESRC Centre on Economics Learning and Social Evolution.
    10. Eshel, Ilan & Samuelson, Larry & Shaked, Avner, 1998. "Altruists, Egoists, and Hooligans in a Local Interaction Model," American Economic Review, American Economic Association, vol. 88(1), pages 157-179, March.
    11. P. Young, 1999. "The Evolution of Conventions," Levine's Working Paper Archive 485, David K. Levine.
    12. Simon Gachter & Ernst Fehr, 2000. "Cooperation and Punishment in Public Goods Experiments," American Economic Review, American Economic Association, vol. 90(4), pages 980-994, September.
    13. Wolfgang Leininger, 2006. "Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 713-719, November.
    14. Ben Cooper & Chris Wallace, 2004. "Group selection and the evolution of altruism," Oxford Economic Papers, Oxford University Press, vol. 56(2), pages 307-330, April.
    15. Hammerstein, Peter & Selten, Reinhard, 1994. "Game theory and evolutionary biology," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 28, pages 929-993, Elsevier.
    16. John Maynard Smith, 1998. "The origin of altruism," Nature, Nature, vol. 393(6686), pages 639-640, June.
    17. Carlsson, H. & van Damme, E.E.C., 1993. "Global games and equilibrium selection," Other publications TiSEM 49a54f00-dcec-4fc1-9488-4, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alexandros Rigos & Heinrich H. Nax, 2015. "Assortativity evolving from social dilemmas," Discussion Papers in Economics 15/19, Division of Economics, School of Business, University of Leicester.

    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. Martin Kaae Jensen & Alexandros Rigos, 2018. "Evolutionary games and matching rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 707-735, September.
    2. Hofbauer, Josef & Sorger, Gerhard, 1999. "Perfect Foresight and Equilibrium Selection in Symmetric Potential Games," Journal of Economic Theory, Elsevier, vol. 85(1), pages 1-23, March.
    3. Charness, Gary & Jackson, Matthew O., 2007. "Group play in games and the role of consent in network formation," Journal of Economic Theory, Elsevier, vol. 136(1), pages 417-445, September.
    4. , 2021. "The Value of a Coordination Game," SocArXiv ymzrd_v1, Center for Open Science.
    5. Kolstad, Ivar, 2007. "The evolution of social norms: With managerial implications," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 36(1), pages 58-72, February.
    6. Kets, Willemien & Kager, Wouter & Sandroni, Alvaro, 2022. "The value of a coordination game," Journal of Economic Theory, Elsevier, vol. 201(C).
    7. Lipman, Barton L. & Wang, Ruqu, 2000. "Switching Costs in Frequently Repeated Games," Journal of Economic Theory, Elsevier, vol. 93(2), pages 149-190, August.
    8. Osano, Hiroshi, 1997. "An Evolutionary Model of Corporate Governance and Employment Contracts," Journal of the Japanese and International Economies, Elsevier, vol. 11(3), pages 403-436, September.
    9. Peski, Marcin, 2010. "Generalized risk-dominance and asymmetric dynamics," Journal of Economic Theory, Elsevier, vol. 145(1), pages 216-248, January.
    10. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
    11. Dai, Darong, 2012. "On the Existence and Stability of Pareto Optimal Endogenous Matching with Fairness," MPRA Paper 40560, University Library of Munich, Germany.
    12. Sanjeev Goyal & Fernando Vega-Redondo, 2000. "Learning, Network Formation and Coordination," Econometric Society World Congress 2000 Contributed Papers 0113, Econometric Society.
    13. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    14. , & , & ,, 2008. "Monotone methods for equilibrium selection under perfect foresight dynamics," Theoretical Economics, Econometric Society, vol. 3(2), June.
    15. Shota Fujishima, 2015. "The emergence of cooperation through leadership," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 17-36, February.
    16. DavidP. Myatt & Chris Wallace, 2009. "Evolution, Teamwork and Collective Action: Production Targets in the Private Provision of Public Goods," Economic Journal, Royal Economic Society, vol. 119(534), pages 61-90, January.
    17. Yehuda Levy, 2013. "A Cantor Set of Games with No Shift-Homogeneous Equilibrium Selection," Mathematics of Operations Research, INFORMS, vol. 38(3), pages 492-503, August.
    18. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
    19. Norman, Thomas W.L., 2012. "Equilibrium selection and the dynamic evolution of preferences," Games and Economic Behavior, Elsevier, vol. 74(1), pages 311-320.
    20. Rossella Argenziano & Itzhak Gilboa, 2012. "History as a coordination device," Theory and Decision, Springer, vol. 73(4), pages 501-512, October.

    More about this item

    Keywords

    Evolutionary Game Theory; Evolutionarily Stable Strategy; ESS; Group Selection; Non-random Matching;
    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:bir:birmec:13-05. 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: Oleksandr Talavera (email available below). General contact details of provider: https://edirc.repec.org/data/debhauk.html .

    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.