Time consistent equilibria in dynamic models with recursive payoffs and behavioral discounting

Abstract

We prove existence of time consistent equilibria in a wide class of dynamic models with recursive payoffs and generalized discounting involving both behavioral and normative applica-tions. Our generalized Bellman equation method identifies and separates both: recursive andstrategic aspects of the equilibrium problem and allows to precisely determine the sufficientassumptions on preferences and stochastic transition to establish existence. In particular we show existence of minimal state space stationary Markov equilibrium (a time-consistent solution) in a deterministic model of consumption-saving with beta-delta discounting andits generalized versions involving magnitude effects, non-additive payoffs, semi-hyperbolic or hyperbolic discounting (over possibly unbounded state and unbounded above reward space). We also provide an equilibrium approximation method for a hyperbolic discounting model.