Replicator dynamics in a Cobweb model with rationally heterogeneous expectations

This paper extends the adaptively rational equilibrium dynamics of Brock and Hommes [Brock, W.A., Hommes, C.H., 1997. A rational route to randomness. Econometrica 65, 1059–1160] by introducing a generalized version of the replicator dynamic. The replicator equilibrium dynamics (RED) couples the price dynamics of a Cobweb model with predictor selection governed by an evolutionary replicator dynamic. We show that the RED supports the conclusion of Sethi and Franke [Sethi, R., Franke, R., 1995. Behavioural heterogeneity under evolutionary pressure: macroeconomic implications of costly optimisation. The Economic Journal, 105, 583–600] that costly rational beliefs persist, though unlike them, these results obtain in the deterministic case. Numerical evidence shows that complex dynamics exist, as in Brock and Hommes, even though no weight is placed on strictly dominated predictors in an RED steady-state.