Recursive equilibrium with Price Perfect Foresight and a minimal state space

This paper analyzes general equilibrium models with finite heterogeneous agents who anticipate future prices through a price expectation function with or without accuracy. I show the existence of a recursive equilibrium with a minimal state space through the Kakutani–Fan–Glicksberg fixed point theorem. Moreover, any such recursive equilibrium implements a sequential equilibrium and its uniqueness implies its continuity. Particularly, I prove that an agent making persistent errors in the price expectation function is driven out of the market in any sequential equilibrium implemented by a continuous recursive equilibrium. This result is established under the condition that exogenous variables converge in probability and assuming that the relative variability of all stochastic discount factors is low. Copyright Springer-Verlag Berlin Heidelberg 2016