A Dual Self Model of Impulse Control

Abstract

Abstract:We propose that a simple "dual-self" model gives a unified explanation for several empirical regularities, including the apparent time-inconsistency that has motivated models of quasi-hyperbolic discounting and Rabin's paradox of risk aversion in the large and small. The model also implies that self-control costs imply excess delay, as in the O'Donoghue and Rabin models of quasi-hyperbolic utility, and it explains experimental evidence that increased cognitive load makes temptations harder to resist. The base version of our model is consistent with the Gul-Pesendorfer axioms, but we argue that these axioms must be relaxed to account for the effect of cognitive load. 1 "The idea of self-control is paradoxical unless it is assumed that the psyche contains more than one energy system, and that these energy systems have some degree of independence from each other." (McIntosh [1969]) This paper argues that a simple "dual-self" model gives a unified explanation for a number of empirical regularities related to self-control problems and a value for commitment in decision problems. One of these regularities is the apparent time inconsistency that has motivated economists' models of quasi-hyperbolic discounting: Faced with a choice between consuming some quantity today and a greater quantity tomorrow, some people will choose to consume the lesser quantity today. However, when these same individuals are faced with the choice between the same relative quantities a year from now and a year and a day from now, they choose to consume the greater quantity a year and a day from now.3 A second regularity is Rabin's [2000] paradox of risk aversion in the large and small. The paradox is that the risk aversion experimental subjects show to very small gambles implies hugely unrealistic willingness to reject large but favorable gambles. In addition, the model provides a possible explanation of the effect of cognitive load on self-control that is noted by Shiv and Fedorkin, and it predicts that increased costs of self-control lead to increased delay in stationary stopping-time problems, as in O'Donoghue and Rabin [2001].2 Our theory proposes that many sorts of decision problems should be viewed as a game between a sequence of short-run impulsive selves and a long-run patient self. This is consistent with recent evidence from MRI studies, such as McClure, Laibson, Loewenstein, and Cohen [2004], that suggests that short-term impulsive behavior is associated with different areas of the brain than long-term planned behavior. 4 We argue that our dual-selves model explains a broad range of behavioral anomalies, and that it is a better (though still crude 5 ) fit for the modular structure of the brain than the quasi-hyperbolic model, which posits a game between multiple "selves," one in each period. Moreover, the dual-selves model is analytically simpler than the quasi-hyperbolic discounting model, as the equilibria of the model can be calculated as the solution to a decision problem. In addition, in standard economic applicatio...

Quantum Type Indeterminacy in Dynamic Decision-Making: Self-Control through Identity Management

“…In this respect, we stand closer to Benabou and Tirole [19]. In particular, we do not address the question related to taking actions (commitment) to limit future behavior as in Gul and Pesendorfer [20] and Fudenberg and Levine [23]. In the next section we briefly return to this question.…”

“…The utility of playing a 1 is U θ 2 (a 1 ) = 2 in the first period plus the expected utility of the second period. To calculate the latter, we first express the type vector |s 0 in terms of |τ i eigenvectors: s 0 = λ 1 (α 1 |τ 1 + α 2 |τ 2 ) + λ 2 (β 1 |τ 1 + β 2 |τ 2 ) = (λ 1 α 1 + λ 2 β 1 ) |τ 1 + (λ 1 α 2 + λ 2 β 2 ) |τ 2 23 Remember that the coefficients of superposition are amplitudes of probability which can take negative values, and that Bohr's rule calls for squaring them to obtain the probability for the corresponding eigentype. 24 Note that the assumption of "a 1 " is not fully arbitrary since a 1 gives a higher utility to θ 1 than a 2 .…”

“…We have recently witnessed renewed interest among prominent economic theorists in the issue of self-control and dynamic inconsistency in decision-making (see e.g., [20][21][22][23][24]). There is a significant theoretical literature pioneered by Strotz [25] dealing with various forms of dynamic inconsistency.…”

“…Various ways to model those selves and the interactions between them have been investigated. Fudenberg and Levine [23,24] develop a dual-self 7 Although this paper uses elements of the quantum formalism in games, we are not dealing with so-called quantum games which study how the extension of classical moves to quantum ones can affect the analysis of the game. That approach consists in changing the strategy space, see for instance [17].…”

The Resolution Game: A Dual Selves Perspective

“…Their cost structure is of zero-infinite type dependent on the mode and so differs from ours: our costs increase continuously with the extent of commitment and cant be infinite. Fudenberg and Levine [6] offer different mechanisms of self-control depending on setting. This might be the choice of the preferences for the myopic self by the long-run self, the limiting of the alternatives available to the short-run self or the long-run self incurring short-run costs to reduce future self control costs.…”