Costly self-control and limited willpower
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Costly self-control and limited willpower Meng-Yu Liang1 · Simon Grant2
· Sung-Lin Hsieh3
Received: 24 February 2019 / Accepted: 30 September 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
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. Keywords Temptation · Self-control · Willpower · Revealed preference JEL Classifications D81 · D91 · D11
Liang would like to acknowledge financial support from Taiwan’s Ministry of Science and Technology under Grant MOST 105-2410-H-001-012.
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Simon Grant [email protected] Meng-Yu Liang [email protected] Sung-Lin Hsieh [email protected]
1
Institute of Economics, Academia Sinica, Taipei, Taiwan
2
Australian National University, Canberra, ACT, Australia
3
Department of Economics, University of Michigan, Ann Arbor, MI, USA
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M.-Y. Liang et al.
1 Introduction Self-control, as the psychologists Muraven and Baumeister (2000) put it, “involves overriding or inhibiting competing urges, behaviors or desires.” Gailliot and Baumeister (2007) describe it as “the conscious and effortful form of self-regulation.” Furthermore, they report physiological research that indicates exercise of such selfcontrol relies on some sort of limited energy source. This can be viewed as providing a physiological foundation to the metaphoric concept of an individual’s (cognitive) resource of willpower. In this paper we propose the following representation for preferences over menus of lotteries that captures this notion of a limited stock of willpower: U (A) = max x∈A [u (x) + v (x)] − max y∈A v (y) , s.t. v (x) max y∈A v (y) − w,
(1)
where A is a (compact) set of lotteries with generic elements denoted by x and y, u and v are von Neumann–Morgenstern utility functions over lotteries that describe the individual’s commitment ranking and temptation ranking, respectively, and a nonnegative number w, that measures the individual’s stock of willpower. This is the representation characterized by Gul and Pesendorfer (2001) (hereafter, GP) with the addit
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