Sleepiness, choice consistency, and risk preferences

Total sleep deprivation studies are a more common approach to studying how sleepiness affects performance and decisions. However, circadian mismatch is a milder, and arguably more externally valid, way to examine sleepiness of the sort commonly experienced by real-world decision makers. Having to be awake at a time of day that is not optimal is more common and may affect performance in a less extreme manner than it would following 24 or more hours of total sleep deprivation in a relatively foreign sleep laboratory environment.

Our sample is 95.9 % comprising young adults between 18 and 25 years old (99 % between 18 and 36 years old).

It is also true that validated morning-type individuals are much more rare in young adult populations, such as our college student samples (Chelminski et al. 1997, 2000). Therefore, we recruit a higher proportion of the morning-types available in our student populations in order to achieve roughly equal numbers of morning-type and evening-type subjects in our final sample.

Similarly, deviations from expected utility theory (EU) and rank-dependent utility theory with a concave utility function are also statistically similar across groups. These results are presented in Appendix 2C. We also examine whether subjects violate payoff dominance in making choices and, while both groups display some violations, there is no difference in violations between groups. In our data, consistency with rationality is robust.

This other stream of research has shown that individuals with higher levels of permanent cognitive ability display an increased propensity to take monetary risk. While interesting, this is fundamentally distinct from our question of how temporary depletion of available cognitive resources will impact risky choice and/or rationality.

Our design includes 50 decisions per subject and provides more statistical power, which increases our confidence in the finding that rationality is not altered by our manipulation. Also, in our design, participants were randomly assigned to treatments (circadian mismatched or matched), and this reduces the possibility that participants self-select into the experiment based on certain characteristics (e.g., rationality).

We are grateful to Sachar Kariv for providing us with the code for the experiment task. Subject instructions for the experiment are included in Appendix 1.

For the first eight sessions, the X and Y intercepts were constrained to lie in the [50, 100] interval (see Fig. 1). For the latter eight sessions, in order to generate more extreme relative prices, the budgets were chosen among the set of lines that intersect both axes below 100 and intersect at least one axis at or above the 50-token level. The initial starting point for the mouse-pointer along each budget line was also randomly determined. See Choi et al. (2007) for full details.

To be more specific, depletion of cognitive resources would disproportionately affect executive function. The behavioral effects reported in the aforementioned studies either involve increased reliance on heuristics (i.e., stereotyping and transference effect) or decreased ability to engage in strategic reasoning (i.e., the guessing game), both of which are consistent with reduced engagement of deliberate thought regions of the brain that rely on fully intact cognition.

Due to the rarity of true morning-type subjects—less than 10 % in young adult populations are morning-types (see Chelminski et al. 2000)—we extend our rMEQ cutoff to include rMEQ scores of 15–17. To compensate, we only recruit the more extreme (and still abundant) evening-type subjects with rMEQ scores from 4 to 10. In this way, our sample is still drawn from the tails of the rMEQ distribution and eliminates the same amount of support from the non-tail portion of the rMEQ distribution compared to if we had used the traditional morning-type cutoff (rMEQ = 18) but included non-extreme evening types (rMEQ = 11) in our sample.

One-hundred and thirty-seven matched subjects signed up for experimental sessions, and 115 showed up. One-hundred and ten mismatched subjects signed up for experimental sessions, and 87 showed up.

There is no a priori reason why sleepy subjects would be expected to make faster or slower decisions. While some dual systems frameworks identify longer response times with more deliberate thinking, in the case of sleepiness, longer response times might also reflect difficulty focusing on the decisions. A recent theoretical framework of response times (Achtziger and Alós-Ferrer 2014) allows an initial stage of decision making where individuals first decide whether to use automatic or deliberative thinking. As such, overall response times are not suitable for identifying whether individuals are using more automatic or deliberative thought processes in our design, which was never intended to produce such informative response time data. Mismatched subjects are slower in responding when relative prices for the two assets are close to one. This could reflect that sleepiness makes it more difficult to choose between similar options or could reflect some kind of indifference that is exacerbated for sleepy subjects (Krajbich et al. 2015, document slower response times for decisions over options for which a subject may be indifferent). The median response time of matched subjects is 7 s and the median response time of mismatched subjects is 8 s.

Additional tests of rationality (expected utility and rank-dependent utility with a concave utility function) produce the same results. More information and technical details on the tests we performed are given in Appendix 2C. The main conclusion is that we find no significance difference between matched and mismatched subjects using a variety of definitions of rationality or adherence to common utility preference frameworks.

We only consider positive prices in all the analyses in the paper. Out of the 10,100 choices made in the experiment (50 choices per subject \(\times \) 202 subjects), 10,094 were with strictly positive prices as our failure to constrain the random price choice in the parameterization of the experiment inadvertently led to 6 instances of zero-priced assets.

We use the log because it gives the percentage change of relative prices [e.g., log(1.10) \(\approx \) 0.10].

Given the mouse-driven graphical choice interface, one might think that sleepy subjects would be less likely to choose safe asset bundles due to motor skill deficits resulting from fatigue. We note that this is not likely the case in our data. However, because that argument would imply that these same sleepy subjects are more likely to choose extreme border asset bundles. This is not the case in our data.

If we add a dummy variable for being female as an additional control in the regressions in Table 4, our main results still hold. The coefficient on being mismatched is 0.082 (p value \(=\) 0.000 in the non-bootstrapped regressions and \(=\)0.062 in the bootstrapped regressions) and the coefficient on female is −0.023 (p value \(=\) 0.059 in non-bootstrapped regression and \(=\)0.602 in the bootstrapped regressions). Women are more risk averse than men, but the effect is not always significant. Results are also robust if we control for amount of sleep the night before the experiment or the subject’s CRT score.

As a robustness check, we evaluate our results on the differences in certainty equivalents between matched and mismatched subjects by also constraining the sample to subjects whose CCEI is close to one. Our main result, that matched subjects are more risk averse, still holds. The result is no longer statistically significant though, and that is a reflection of the smaller number of observations in the constrained sample.

The Tobit regression takes the calculated certainty equivalent for an individual for a given lottery and regresses it on a dummy variable for being mismatched. There are 361 possible generated lotteries for each individual and 202 individuals, yielding 72,922 observations, and the regressions cluster at the individual level.

In particular, suppose a person is observed choosing allocation (x,y) in menu 1 and (a,b) in menu 2 for an experiment with two essential Arrow–Debreu securities. The observed quantities in this experiment are A = {0,x,y,a,b} and the associated lattice to the experiment is A\(\times \)A. A preference relation can be extended to this lattice by checking whether x in A\(\times \)A was affordable when (x,y) in menu 1 was chosen or when (a,b) in menu 2 was chosen.

\(\lambda _{1k}=\lambda _{2k}\) whenever \(\hbox {x}_{1\mathrm{k}}\) and \(\hbox {x}_{2\mathrm{k}}\) are different. These numbers are restricted to be positive.

\(\hbox {w}_{1\mathrm{k}} = \hbox {w}_{2\mathrm{k}}\) if \(\hbox {p}_{1\mathrm{k}}= \hbox {p}_{2\mathrm{k}} = 1/2\). Only one of the two numbers is necessary if \(\hbox {x}_{1\mathrm{k}}\) and \(\hbox {x}_{2\mathrm{k}}\) are different.

The normalization is possible because the inequalities are homogeneous of degree one in u and \(\lambda \).