Self-control and bargaining

This paper examines a bargaining game with alternating proposals where sophisticated quasi-hyperbolic discounters negotiate over an infinite stream of payoffs. In Markov perfect equilibrium, payoffs are almost always unique, and a small advantage in self-control can result in a large advantage in payoff. In subgame-perfect equilibrium, a multiplicity of payoffs and delay can arise, despite the complete information setting. Markov perfect equilibria are the best subgame-perfect equilibria for the agent with more self-control, and the worst for the agent with less self-control. Naïveté can help a player by increasing their reservation value.