Evolution and correlated equilibrium

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.