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Evolution and correlated equilibrium

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Abstract

Given a normal form game and a signal generating process, we construct an expanded game in the spirit of Aumann (Econometrica 55(1):1–18, 1987) in which agents condition their strategic choices on perceived signals. We collect results on evolutionary selection dynamics of Ritzberger and Weibull (Econometrica 63(6):1371–1399, 1995), Swinkels (J Econ Theory 57(2):306–332, 1992b) and Samuelson and Zhang (J Econ Theory 57:363–391, 1992) to apply them to normal form games with payoff irrelevant signals. We suggest a selection dynamic for the evolution of signals and characterize the set of signal distributions and induced payoffs for sets that are asymptotically stable with respect to this evolutionary selection on signals.

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Notes

  1. The concept of evolutionary game theory originates from biology. See Dawkins (1990) or Björnerstedt and Weibull (1996) for socio-economic interpretations.

  2. See Hart and Mas-Colell (2000), p. 1132 “(4) ... This implies, in particular, that interior (relative to Δ(S)) points of the set of correlated equilibria that are not pure Nash equilibria are unreachable as the limit of some z t [, the empirical distribution of play.] ...”

  3. Proposition 2 in Lenzo and Sarver (2006)

  4. By the Picard-Lindelöf Theorem, there exists a unique solution \(\hat \rho (\cdot ,\rho )\) for each initial condition \(\rho \in {\Delta }_{\mathcal {R}}\); see Weibull (1995) pp.232.

  5. See also Swinkels (1992a), p.315

  6. More technically, the suggestion is to increase the probability mass π(γ ′) or to decrease the probability mass π(γ ″).

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Authors and Affiliations

  1. TU Dortmund University, Dortmund, Germany

    Lars P. Metzger

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  1. Lars P. Metzger
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Correspondence to Lars P. Metzger.

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Metzger, L.P. Evolution and correlated equilibrium. J Evol Econ 28, 333–346 (2018). https://doi.org/10.1007/s00191-017-0539-z

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  • DOI: https://doi.org/10.1007/s00191-017-0539-z

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