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The evolution of the mixed conjectures in the rent-extraction game

Author

Listed:
  • Paulo Brito
  • Bipasa Datta
  • Huw Dixon
Abstract
This paper adopts an evolutionary perspective on the rent-extraction model with conjectural variations (CV) allowing for mixed-strategies. We analyze the dynamics of the model with n 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. Further, we develop a more general notion of consistency which applies to mixed-strategy equilibria. In a three conjecture example, by conducting a global dynamics analysis, we prove 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 (both eigenvalues positive), or saddle-stable (one stable eigenvalue). There also exist heteroclinic orbits that link equilibria together. Whilst only the pure-strategies can be fully consistent, we find a lower bound for the probability that mixed strategy conjectures will be ex post consistent.

Suggested Citation

  • Paulo Brito & Bipasa Datta & Huw Dixon, 2012. "The evolution of the mixed conjectures in the rent-extraction game," Discussion Papers 12/33, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:12/33
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    References listed on IDEAS

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    Cited by:

    1. Kopel, Michael & Lamantia, Fabio & Szidarovszky, Ferenc, 2014. "Evolutionary competition in a mixed market with socially concerned firms," Journal of Economic Dynamics and Control, Elsevier, vol. 48(C), pages 394-409.
    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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