Time Preferences and Bargaining

This paper presents an analysis of general time preferences in the canonical Rubinstein (1982) model of bargaining, allowing for arbitrarily history-dependent strategies. I derive a simple sufficient structure for optimal punishments and thereby fully characterize (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 characterization, 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.