IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v77y2015icp55-61.html
   My bibliography  Save this article

Conjectural variations in aggregative games: An evolutionary perspective

Author

Listed:
  • Possajennikov, Alex

Abstract

Suppose that in symmetric aggregative games, in which payoffs depend only on a player’s strategy and on an aggregate of all players’ strategies, players have conjectures about the reaction of the aggregate to marginal changes in their strategy. The players play a conjectural variation equilibrium, which determines their fitness payoffs. The paper shows that only consistent conjectures can be evolutionarily stable in an infinite population, where a conjecture is consistent if it is equal to the marginal change in the aggregate determined by the actual best responses. In the finite population case, only zero conjectures representing aggregate-taking behavior can be evolutionarily stable.

Suggested Citation

  • Possajennikov, Alex, 2015. "Conjectural variations in aggregative games: An evolutionary perspective," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 55-61.
    • Handle: RePEc:eee:matsoc:v:77:y:2015:i:c:p:55-61
    DOI: 10.1016/j.mathsocsci.2015.07.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165489615000670
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.mathsocsci.2015.07.003?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Müller, W. & Normann, H.T., 2003. "Conjectural Variations and Evolutionary Stability : A New Rationale for Consistency," Other publications TiSEM af576ec2-1637-4390-8b59-1, Tilburg University, School of Economics and Management.
    2. Heifetz, Aviad & Shannon, Chris & Spiegel, Yossi, 2007. "What to maximize if you must," Journal of Economic Theory, Elsevier, vol. 133(1), pages 31-57, March.
    3. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    4. Martin K. Perry, 1982. "Oligopoly and Consistent Conjectural Variations," Bell Journal of Economics, The RAND Corporation, vol. 13(1), pages 197-205, Spring.
    5. Dixon, Huw D. & Somma, Ernesto, 2003. "The evolution of consistent conjectures," Journal of Economic Behavior & Organization, Elsevier, vol. 51(4), pages 523-536, August.
    6. Possajennikov, Alex, 2009. "The evolutionary stability of constant consistent conjectures," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 21-29, October.
    7. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(3), pages 497-516, October.
    8. Morton I. Kamien & Nancy L. Schwartz, 1983. "Conjectural Variations," Canadian Journal of Economics, Canadian Economics Association, vol. 16(2), pages 191-211, May.
    9. Alex Possajennikov, 2003. "Evolutionary foundations of aggregate-taking behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(4), pages 921-928, June.
    10. Itaya, Jun-ichi & Dasgupta, Dipankar, 1995. "Dynamics, Consistent Conjectures, and Heterogeneous Agents in the Private Provision of Public Goods," Public Finance = Finances publiques, , vol. 50(3), pages 371-389.
    11. Wieland Müller & Hans-Theo Normann, 2005. "Conjectural Variations and Evolutionary Stability: A Rationale for Consistency," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 161(3), pages 491-502, September.
    12. Wieland Müller & Hans-Theo Normann, 2007. "Conjectural variations and evolutionary stability in finite populations," Journal of Evolutionary Economics, Springer, vol. 17(1), pages 53-61, February.
    13. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
    14. Cornes, Richard & Hartley, Roger, 2012. "Fully aggregative games," Economics Letters, Elsevier, vol. 116(3), pages 631-633.
    15. Makowski, Louis, 1987. "Are 'Rational Conjectures' Rational?," Journal of Industrial Economics, Wiley Blackwell, vol. 36(1), pages 35-47, September.
    16. Bresnahan, Timothy F, 1981. "Duopoly Models with Consistent Conjectures," American Economic Review, American Economic Association, vol. 71(5), pages 934-945, December.
    17. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
    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. Joseph Farrell & Jonathan B. Baker, 2021. "Natural Oligopoly Responses, Repeated Games, and Coordinated Effects in Merger Analysis: A Perspective and Research Agenda," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 58(1), pages 103-141, February.
    2. Wolfgang Buchholz & Todd Sandler, 2017. "Successful Leadership in Global Public Good Provision: Incorporating Behavioural Approaches," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 67(3), pages 591-607, July.
    3. Alex Possajennikov, 2016. "Evolution of Consistent Conjectures in Semi-Aggregative Representation of Games, with Applications to Public Good Games and Contests," Discussion Papers 2016-08, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    4. Adamson, Jordan & Wilson, Bart J., 2024. "Territory in the state of nature," Journal of Economic Behavior & Organization, Elsevier, vol. 219(C), pages 490-509.
    5. Aloys L. Prinz, 2019. "Indirect Evolution and Aggregate-Taking Behavior in a Football League: Utility Maximization, Profit Maximization, and Success," Games, MDPI, vol. 10(2), pages 1-12, May.

    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. Ilkka Leppänen, 2018. "Evolutionarily stable conjectures and other regarding preferences in duopoly games," Journal of Evolutionary Economics, Springer, vol. 28(2), pages 347-364, April.
    2. Prof. Jean-Paul Chavas, 2010. "On Industry Structure and Firm Conduct in Long Run Equilibrium," Journal of Management and Strategy, Journal of Management and Strategy, Sciedu Press, vol. 1(1), pages 2-21, December.
    3. Leppänen, Ilkka, 2016. "Consistent conjectures and the evolutionary stability of other-regarding preferences," Economics Letters, Elsevier, vol. 142(C), pages 53-55.
    4. Matthew McGinty, 2021. "Rational conjectures and evolutionary beliefs in public goods games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(6), pages 1130-1143, December.
    5. Paulo Brito & Bipasa Datta & Huw Dixon, 2011. "The evolution of mixed conjectures in the rent-extraction game," Discussion Papers 11/06, Department of Economics, University of York.
    6. Burkhard C. Schipper, 2021. "The evolutionary stability of optimism, pessimism, and complete ignorance," Theory and Decision, Springer, vol. 90(3), pages 417-454, May.
    7. N. Quérou & M. Tidball, 2014. "Consistent conjectures in a dynamic model of non-renewable resource management," Annals of Operations Research, Springer, vol. 220(1), pages 159-180, September.
    8. Iskakov, A. & Iskakov, M., 2017. "In Search of a Generalized Concept of Rationality," Journal of the New Economic Association, New Economic Association, vol. 34(2), pages 181-189.
    9. Possajennikov, Alex, 2009. "The evolutionary stability of constant consistent conjectures," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 21-29, October.
    10. Figuieres, Charles & Tidball, Mabel & Jean-Marie, Alain, 2004. "On the effects of conjectures in a symmetric strategic setting," Research in Economics, Elsevier, vol. 58(1), pages 75-102, March.
    11. Dixon, Huw D. & Somma, Ernesto, 2003. "The evolution of consistent conjectures," Journal of Economic Behavior & Organization, Elsevier, vol. 51(4), pages 523-536, August.
    12. Andreas Hefti & Julian Teichgräber, 2021. "Inequality in models with a competition for market shares," ECON - Working Papers 375, Department of Economics - University of Zurich.
    13. Friedman, James W. & Mezzetti, Claudio, 2002. "Bounded rationality, dynamic oligopoly, and conjectural variations," Journal of Economic Behavior & Organization, Elsevier, vol. 49(3), pages 287-306, November.
    14. Luis C. Corchón, 2021. "Aggregative games," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(1), pages 49-71, March.
    15. Birgitte Sloth & Hans Whitta-Jacobsen, 2011. "Economic Darwinism," Theory and Decision, Springer, vol. 70(3), pages 385-398, March.
    16. Vanzetti, David & Kennedy, John O.S., 1989. "Optimal Retaliation in International Commodity Markets," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 57(01-02-03), pages 1-25, December.
    17. Holloway, Garth J., 1992. "The Representative Firm, Endogenous Output Decisions And Consistent Conjectural Variations In Oligopoly," Working Papers 225876, University of California, Davis, Department of Agricultural and Resource Economics.
    18. Holloway, Garth J., 1992. "Consistent Conjectures In Symmetric Equilibria," Working Papers 225873, University of California, Davis, Department of Agricultural and Resource Economics.
    19. Ludovic A. Julien, 2010. "From Imperfect To Perfect Competition: A Parametric Approach Through Conjectural Variations," Manchester School, University of Manchester, vol. 78(6), pages 660-677, December.
    20. Nocetti, Diego & Smith, William T., 2015. "Changes in risk and strategic interaction," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 37-46.

    More about this item

    JEL classification:

    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:eee:matsoc:v:77:y:2015:i:c:p:55-61. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.