Time Preferences and Bargaining

Abstract

This paper presents an analysis of general time preferences in the canonical Rubin- stein (1982) model of bargaining, allowing for arbitrarily history-dependent strategies. I derive a simple sufficient structure for optimal punishments and thereby fully charac- terize (i) the set of equilibrium outcomes for any given preference profile, and (ii) the set of preference profiles for which equilibrium is unique. Based on this characteri- zation, I establish that a weak notion of present bias—implied, for example, by any hyperbolic or quasi-hyperbolic discounting—is sufficient for equilibrium to be unique, stationary, and efficient. Conversely, I demonstrate how certain violations of present bias give rise to multiple (non-stationary) equilibria that feature delayed agreement under gradually increasing offers.