Optimal Discounting∗

The agent is modelled as a current self that optimally incurs a cognitive cost of empathizing with future selves. The model unifies well-known experimental and empirical findings in intertemporal choice and enriches the multiple selves model with a notion of self-control. The defining feature of the model is magnitude-decreasing impatience: greater patience towards larger rewards. Two behavioral definitions of magnitude-decreasing impatience are provided and the model is characterized under each of them.