Models of limited self-control: Comparison and implications for bargaining

•Fudenberg and Levine's dual-self model (2006) is compared with β-δ discounting.•Fudenberg and Levine (FL) agents care about future self-control costs.•β-δ agents can be viewed as FL agents that do not care about such costs.•The models' differing implications are compared in a bargaining game.

This paper compares two models of limited intertemporal self-control: the linear-cost version of Fudenberg and Levine's dual-self model (2006) and the quasi-hyperbolic discounting model. The main distinction between the two frameworks can be formulated as whether agents care about future self-control costs: dual selves do, while quasi-hyperbolic discounters do not. The dual-self model is applied to a bargaining game with alternating proposals where players negotiate over an infinite stream of payoffs, and it is shown that, in subgame-perfect equilibrium, the first proposer's payoff is unique and agreement is immediate. By contrast, Lu (2016) shows that with quasi-hyperbolic discounters, a multiplicity of payoffs and delay can arise in equilibrium.