Costly self-control and limited willpower

Abstract

In Gul and Pesendorfer (Econometrica 69(6):1403–1435, 2001), a decision-maker, when facing a choice among menus, evaluates each menu in terms of the maximum value of its commitment utility net of self-control costs. This paper extends the model such that this maximum is constrained by the condition that the cost of self-control cannot exceed the decision-maker’s stock of willpower w. Four of the five axioms of our characterization are as in their Theorem 3 except that the independence axiom is restricted to a subset of menus. We add one new axiom to regulate willpower as a limited (cognitive) resource in which the available “stock” does not vary across menus. In our characterization, choices within menus that satisfy WARP reveal a constant trade-off between commitment and temptation utilities. However, it is the discontinuity of preferences over menus (along with violations of WARP for choices within menus) that reveals w (measured in units of temptation utility), allowing for a behaviorally meaningful comparative measure of self-control across individuals.