IDEAS home Printed from https://ideas.repec.org/p/not/notecp/12-04.html
   My bibliography  Save this paper

Conjectural Variations in Aggregative Games: An Evolutionary Perspective

Author

Listed:
  • Alex Possajennikov

Abstract

Suppose that in aggregative games, in which a player's payoff depends only on this player's strategy and on an aggregate of all players' strategies, the players are endowed with constant conjectures about the reaction of the aggregate to marginal changes in the player's strategy. The players play the equilibrium determined by their conjectures and equilibrium strategies determine the players' payoffs, which can be different for players with different conjectures. It is shown that with random matching in an infinite population, only consistent conjectures can be evolutionarily stable, where a conjecture is consistent if it is equal to the marginal change in the aggregate at equilibrium, determined by the players' actual best responses. In the finite population case in which relative payoffs matter, only zero conjectures representing aggregate-taking behavior can be evolutionarily stable. The results are illustrated with the examples of a linear-quadratic game (that includes a Cournot oligopoly) and a rent-seeking game.

Suggested Citation

  • Alex Possajennikov, 2012. "Conjectural Variations in Aggregative Games: An Evolutionary Perspective," Discussion Papers 12/04, University of Nottingham, School of Economics.
    • Handle: RePEc:not:notecp:12/04
    as

    Download full text from publisher

    File URL: https://www.nottingham.ac.uk/economics/documents/discussion-papers/12-04.pdf
    Download Restriction: no
    ---><---

    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. 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.
    3. 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.
    4. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599, November.
    5. 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.
    6. Morton I. Kamien & Nancy L. Schwartz, 1983. "Conjectural Variations," Canadian Journal of Economics, Canadian Economics Association, vol. 16(2), pages 191-211, May.
    7. Acemoglu, Daron & Jensen, Martin Kaae, 2013. "Aggregate comparative statics," Games and Economic Behavior, Elsevier, vol. 81(C), pages 27-49.
    8. 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.
    9. Martin K. Perry, 1982. "Oligopoly and Consistent Conjectural Variations," Bell Journal of Economics, The RAND Corporation, vol. 13(1), pages 197-205, Spring.
    10. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
    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. Possajennikov, Alex, 2009. "The evolutionary stability of constant consistent conjectures," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 21-29, October.
    13. 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.
    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. 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.
    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. 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. 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.
    4. Leppänen, Ilkka, 2016. "Consistent conjectures and the evolutionary stability of other-regarding preferences," Economics Letters, Elsevier, vol. 142(C), pages 53-55.
    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. Dixon, Huw D. & Somma, Ernesto, 2003. "The evolution of consistent conjectures," Journal of Economic Behavior & Organization, Elsevier, vol. 51(4), pages 523-536, August.
    10. Possajennikov, Alex, 2009. "The evolutionary stability of constant consistent conjectures," Journal of Economic Behavior & Organization, Elsevier, vol. 72(1), pages 21-29, October.
    11. Andreas Hefti & Julian Teichgräber, 2021. "Inequality in models with a competition for market shares," ECON - Working Papers 375, Department of Economics - University of Zurich.
    12. 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.
    13. 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.
    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. 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.
    18. Turnovsky, Stephen J & Basar, Tamer & d'Orey, Vasco, 1988. "Dynamic Strategic Monetary Policies and Coordination in Interdependent Economies," American Economic Review, American Economic Association, vol. 78(3), pages 341-361, June.
    19. 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.
    20. Holloway, Garth J., 1992. "Consistent Conjectures In Symmetric Equilibria," Working Papers 225873, University of California, Davis, Department of Agricultural and Resource Economics.

    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:not:notecp:12/04. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/denotuk.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.