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

Paulo Brito (), Bipasa Datta and Huw Dixon

Discussion Papers from Department of Economics, University of York

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.

Keywords: Rent-extraction; evolutionary dynamics; consistent conjectures; global dynamics; mixed-strategy (search for similar items in EconPapers)
JEL-codes: D03 H0 L15 (search for similar items in EconPapers)
Date: 2012-12
New Economics Papers: this item is included in nep-evo, nep-gth and nep-hpe
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Citations: View citations in EconPapers (2)

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Related works:
Working Paper: The evolution of mixed conjectures in the rent-extraction game (2012) Downloads
Working Paper: The evolution of mixed conjectures in the rent-extraction game (2011) Downloads
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