On time-inconsistency in bargaining

This paper analyzes dynamically inconsistent time preferences in Rubinstein's (1982) seminal model of bargaining. When sophisticated bargainers have time preferences that exhibit a form of present bias - satisfied by the hyperbolic and quasi-hyperbolic time preferences increasingly common in the economics literature - equilibrium is unique and lacks delay. However, when one bargainer is more patient about a single period's delay from the present than one that occurs in the near future, the game permits a novel form of equilibrium multiplicity and delay. Time preferences with this property have most recently been empirically documented; they can also arise when parties who weight probabilities non-linearly bargain under the shadow of exogenous breakdown risk, as well as in settings of intergenerational bargaining with imperfect altruism. The paper's main contributions are (i) a complete characterization of the set of equilibrium outcomes and payoffs for separable time preferences, and (ii) present bias as a readily interpretable sufficient condition for uniqueness at the level of individual preferences.