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The evolution of mixed conjectures in the rent-extraction game

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  • Paulo Brito
  • Bipasa Datta
  • Huw Dixon

Abstract

This paper adopts an evolutionary perspective on the rent-extraction model with conjectural variations (CV). We analyze the global dynamics of the model with three CVs under the replicator equation. We find that the end points of the evolutionary dynamics include the pure-strategy consistent CVs. However, there are also mixed-strategy equilibria that occur. These are on the boundaries between the basins of attraction of the pure-strategy sinks. We develop a more general notion of consistency which applies to mixed-strategy equilibria. In a three conjecture example, we find that in contrast to the pure-strategy equilibria, the mixed-strategy equilibria are not ESS: under the replicator dynamics, there are three or four mixed equilibria that may either be totally unstable, or saddle-stable. There also exist heteroclinic orbits that link equilibria together.

Suggested Citation

  • 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.
    • Handle: RePEc:yor:yorken:11/06
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    1. Nicola Giocoli, 2005. "The escape from conjectural variations: the consistency condition in duopoly theory from Bowley to Fellner," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 29(4), pages 601-618, July.
    2. 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.
    3. Boyer, Marcel & Moreaux, Michel, 1983. "Consistent versus Non-Consistent Conjectures in Doupoly Theory: Some Examples," Journal of Industrial Economics, Wiley Blackwell, vol. 32(1), pages 97-110, September.
    4. Jean-Marie, Alain & Tidball, Mabel, 2006. "Adapting behaviors through a learning process," Journal of Economic Behavior & Organization, Elsevier, vol. 60(3), pages 399-422, July.
    5. Klemperer, Paul D. & Meyer, Margaret A., 1988. "Consistent conjectures equilibria: A reformulation showing non-uniqueness," Economics Letters, Elsevier, vol. 27(2), pages 111-115.
    6. Menezes, Flavio M. & Quiggin, John, 2010. "Markets for influence," International Journal of Industrial Organization, Elsevier, vol. 28(3), pages 307-310, May.
    7. repec:bla:scandj:v:79:y:1977:i:2:p:210-26 is not listed on IDEAS
    8. Martin K. Perry, 1982. "Oligopoly and Consistent Conjectural Variations," Bell Journal of Economics, The RAND Corporation, vol. 13(1), pages 197-205, Spring.
    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. Margaret E. Slade, 1995. "Empirical Games: The Oligopoly Case," Canadian Journal of Economics, Canadian Economics Association, vol. 28(2), pages 368-402, May.
    12. Bresnahan, Timothy F, 1981. "Duopoly Models with Consistent Conjectures," American Economic Review, American Economic Association, vol. 71(5), pages 934-945, December.
    13. Jun–ichi Itaya & Makoto Okamura, 2003. "Conjectural Variations and Voluntary Public Good Provision in a Repeated Game Setting," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 5(1), pages 51-66, January.
    14. Frank Hahn, 1978. "On Non-Walrasian Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(1), pages 1-17.
    15. Tanaka, Yasuhito, 1991. "On the Consistent Conjectures Equilibrium of Export Subsidy Game," Bulletin of Economic Research, Wiley Blackwell, vol. 43(3), pages 259-271, July.
    16. Cornes, Richard & Sandler, Todd, 1985. "On the consistency of conjectures with public goods," Journal of Public Economics, Elsevier, vol. 27(1), pages 125-129, June.
    17. Dixon, Huw, 1986. "Strategic Investment with Consistent Conjectures," Oxford Economic Papers, Oxford University Press, vol. 38(0), pages 111-128, Suppl. No.
    18. Sugden, Robert, 1985. "Consistent conjectures and voluntary contributions to public goods: why the conventional theory does not work," Journal of Public Economics, Elsevier, vol. 27(1), pages 117-124, June.
    19. Cornes, Richard & Sandler, Todd, 1984. "The theory of public goods: non-nash behaviour," Journal of Public Economics, Elsevier, vol. 23(3), pages 367-379, April.
    20. Szidarovszky, Ferenc & Okuguchi, Koji, 1997. "On the Existence and Uniqueness of Pure Nash Equilibrium in Rent-Seeking Games," Games and Economic Behavior, Elsevier, vol. 18(1), pages 135-140, January.
    21. Robert Michaels, 1989. "Conjectural variations and the nature of equilibrium in rent-seeking models," Public Choice, Springer, vol. 60(1), pages 31-39, January.
    22. 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.
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    Cited by:

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    2. 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.

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    More about this item

    Keywords

    Rent-extraction; evolutionary dynamics; consistent conjectures; global dynamics; mixed-strategy.;
    All these keywords.

    JEL classification:

    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • L15 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Information and Product Quality
    • H0 - Public Economics - - General

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