The evolution of the mixed conjectures in the rent-extraction game
AbstractThis 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.
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Bibliographic InfoPaper provided by Department of Economics, University of York in its series Discussion Papers with number 12/33.
Date of creation: Dec 2012
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Rent-extraction; evolutionary dynamics; consistent conjectures; global dynamics; mixed-strategy;
Find related papers by JEL classification:
- D03 - Microeconomics - - General - - - Behavioral Economics; Underlying Principles
- L15 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Information and Product Quality
- H0 - Public Economics - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-12-22 (All new papers)
- NEP-EVO-2012-12-22 (Evolutionary Economics)
- NEP-GTH-2012-12-22 (Game Theory)
- NEP-HPE-2012-12-22 (History & Philosophy of Economics)
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