ABSTRACT We administer an online Guessing Game collecting responses across all 24 h of the day. While time-of-day itself does not affect guesses, when including trait-level sleepiness and previous night sleep, adverse sleep states lead to responses significantly farther from equilibrium. ARTICL

David L Dickinson

Todd Mcelroy

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Dickinson, David L. and Todd McElroy (2010)  “Rationality Around the Clock:  
Sleep and Time-of-Day Effects on Guessing Game Responses.”  Economics Letters, 
108(2): 245-248. DOI: 10.1016/j.econlet.2010.04.029  Published by Elsevier (ISSN: 
0165-1765)  
 
Rationality Around the Clock:  Sleep and Time-of-Day Effects 
on Guessing Game Responses 
 
David L. Dickinson and Todd McElroy 
 
 
 
 
ABSTRACT 
We administer an online Guessing Game collecting responses across all 24 h of the 
day. While time-of-day itself does not affect guesses, when including trait-level 
sleepiness and previous night sleep, adverse sleep states lead to responses 
significantly farther from equilibrium. 
 
 
 
ARTICLE 
 
1. Introduction 
In industrialized countries, a significant public health concern has been the erosion of 
good sleep habits. At least 25% of adults are considered chronically sleep deprived1, 
and our 24/7 society places increasing demands on individuals at irregular times of the 
day. Travel schedules, shift work, and poor sleep priorities can all deplete cognitive 
resources and together may negatively impact rational decision-making. Sleep 
deprivation has been estimated to cost the U.S. economy $40 billion annually in lost 
worker productivity (Stoller, 1997), and public safety is at risk in some professions 
where sleep loss and irregular scheduling are common (e.g., medical residency and air 
traffic control). Nevertheless, the behavioral effects of adverse sleep states have been 
largely ignored by economists. Current sleep research is now examining which 
components of decision-making are most affected by adverse sleep states, but there is 
a lack of research on decision tasks of interest to economists. 
 
This study explores sleep effects in the p-beauty contest, or “guessing game” (Nagel, 
1995). This well-known game is a building block of more complicated environments 
where iterative reasoning skills are engaged. Decision-making that requires iterative 
reasoning and anticipation of others' behavior is a high-level skill at risk in sleepy 
decision-makers. We report results from a unique experimental design in which subjects 
are recruited to complete an online survey within a randomly assigned one-hour time 
period, and a one-shot Guessing Game is implemented with real financial incentives 
within the survey. Responses are time-stamped for compliance, and other survey 
questions yield measures of the respondent's sleepiness and previous night's sleep. 
Sample selection in our experimental design implies that we likely have a conservate 
estimate of true behavioral effects. Our results show that adverse sleep attributes lead 
to Guessing Game responses consistent with lower levels of iterative reasoning, and 
these behavioral effects grow in magnitude and significance for individuals with multiple 
adverse sleep attributes. 
 
2. Experiments 
Names from student email lists were randomly assigned to a one-hour response 
window on either Tuesday, Wednesday, or Thursday of the experiment week. 
Recruitment emails highlighted the incentives, the survey link, and the randomly 
assigned response time slot. Fig. 1 shows that most subjects responded during their 
assigned time slot. A random prize drawing of $100 ($300 for midnight to 8 a.m. time 
slots) was used as an incentive for completing the survey within the assigned response 
window. The initial recruitment email highlighted that one survey question would also 
offer the chance to win an additional $50. The survey question itself also highlighted the 
additional incentive: 
 
“Please submit an integer number (no decimals) between 0 and 1000 (including 0 and 
1000 as possibilities). All survey respondents this semester will be making this same 
choice. The winner is the person whose chosen number is closest to 2/3 of the average 
number submitted. The winning prize is $50.(in the event of a tie, the prize money will 
be equally shared).” 
 
 
 
 
Fig. 1. Summary of survey responses according to randomly assigned time slot.  
 
The equilibrium guess, 0, is attained by eliminating dominated responses, assuming 
others do so as well, and iterating this process infinitely. For example, all responses > 
667 = 2/3*1000 are dominated and thus eliminated, but a second iteration would 
assume no one should guess above 445 = 2/3*667, and so on. While the survey 
instructions asked subjects to complete the survey themselves with no aids, we have no 
way of verifying compliance. However, one of the survey questions asked subjects to 
indicate the freezing point of vodka (−16.51 °F for 80-proof vodka). The answer is easily 
found with a Google search, yet only about 3.5% of all subjects answered correctly. 
Thus, we feel somewhat confident that subjects respected our survey rules. 
 
3. Results 
A total of 684 subjects completed the survey, with an average 28.5 responses per each 
1-hour time slot of the day (23.5 responses per time slot from 1 a.m.–5 a.m.). Self-
reported state-level sleepiness (i.e., responses to “How sleepy do you feel right now?”) 
in Fig. 2 is generally higher during the night, as expected, even though subjects self-
select into the experiment. Fig. 3 shows mean unconditional Guesses during each 1-
hour response window. 
 
 
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Fig. 2. State-level (Karolinska) Sleepiness Scores by time-of-day.  
 
 
 
 
 
-------------------------------------------------------------------------------- 
 
 
  
 
Fig. 3. Guesses by time-of-day.  
 
 
The key independent variables used to examine Guess levels are the following: 
previous night sleep, trait-level sleepiness, and good/bad time-of-day. The mean 
previous night sleep level was 6.5 h (responses were in intervals (4–5 h, 5–6 h, etc.), 
and coded at the midpoint). We define sleep deprivation as SD = 1 if previous night 
sleep was less than 6 h and SD = 0 if previous night sleep was greater than7 h 
(discarding responses in the interval “6–7 h”, given the greater subjectivity in classifying 
such average responses as either SD = 0 or SD = 1). One's propensity to fall asleep 
during the day (i.e., “trait-level” sleepiness) is generated from a series of 7 questions 
with with 0–3 response scales. We define the dummy variable TSleepy = 1 for scores 
greater than 10, and TSleepy = 0 for scores less than 10 (again, discarding scores of 
the arbitrary cutoff value of 10).2 Finally, time-of-day is split into times associated with 
higher versus lower alertness ratings as established in the literature (see Smith et al., 
2002). We therefore score BadTime = 1 for response times from 1:00 to 5:00 a.m., and 
BadTime = 0 for noon-7 p.m. response times. A correlation of +.18 exist between 
TSleepy and SD (Spearman, p = .01) using these definitions. The Appendix shows the 
relevant online survey questions and Guessing Game instructions that we used to 
generate our dependent and independent variables.3 
 
We proceed using these categorical regressors to examine time-of-day, trait-level 
sleepiness, and previous night sleep. Preliminary regressions retaining the semi-
continuous nature of trait-level sleepiness and previous night sleep variables show they 
lack predictive power, which may not be surprising given that these self-reported 
variables likely contain noise. Our results (below) using categorical variables indicate 
that there are likely important tipping points before these explanatory variables affect 
behavior. 
 
Table 1 reports mean levels of Guess by the different sleep categories. Two-sample t-
tests of mean Guess levels in single-condition comparisons show that GuessSD = 1 > 
GuessSD = 0 (p = .07: one-tailed test), while we cannot reject the hypothesis that mean 
guess levels are identical for subgroups of Badtime = 0 v. Badtime = 1 or TSleepy = 0 v. 
TSleepy = 1. This result is consistent with recent results in Dickinson and McElroy, 2009 
D.L. Dickinson and T. McElroy, Naturally-occurring sleep choice and time of day effects 
on p-beauty contest outcomes, Working paper, Appalachian State University #09-03 
(2009).Dickinson and McElroy (2009), which reported that objectively measured 
voluntary sleep loss lowers the estimated level of iterative reasoning in the Guessing 
Game. We find the same basic result here with our SD variable, though in a distinct 
online (one-shot) experiment with self-reported sleep levels. 
 
 
-------------------------------------------------------------------------------- 
 
Table 1.  
Mean guesses by sleep condition. 
 
Bad 
Mean 
value 
Good 
Mean 
value 
t-value (Good–Bad 
guess difference) 
Single conditions comparisons 
Badtime (n = 94) 397.41 Goodtime (n = 242) 402.08 −0.16 
TSleepy (n = 151) 398.25 Not TSleepy (n = 532) 373.83 1.05 
Last night Sleep-
Deprived (SD) (n = 234) 
396.29 
Last night Well-rested 
(WR) (n = 259) 
363.29 1.47* 
Double-condition comparisons 
Badtime and TSleepy 
(n = 22) 
477.64 
Goodtime and Not TSleepy 
(n = 154) 
394.81 1.34* 
Badtime and Last night 
SD (n = 35) 
443.57 
Goodtime and Last night 
WR (n = 95) 
368.08 1.43* 
TSleepy and Last night 
SD (n = 64) 
414.00 
Not TSleepy and Last night 
WR (n = 216) 
360.82 1.45* 
Triple-condition comparisons 
Badtime and TSleepy 
and Last Night SD 
(n = 12) 
530.08 
Goodtime and Not TSleepy 
and Last night WR (n = 77) 
364.39 1.75** 
*,** Indicate one-tailed statistical significance at the p = .10 and p = .05 levels, respectively. 
For “Double-Condition” comparisons, we compare best-case to worst-case scenarios. 
For example, the first double-condition comparison examines the subset of data where 
both Badtime = 1 and TSleepy = 1 to the subset of data where Badtime = 0 and 
TSleepy = 0. These comparisons show that any pair of “bad” sleep attributes generates 
Guess levels significantly farther from equilibrium compared to an individual with neither 
of the “bad” conditions.4 Though neither BadTime nor TSleepy individually affect Guess 
levels, an individual with both TSleepy = 1and BadTime = 1 has mean Guess level 
farther from equilibrium. Similarly, for the triple-conditions case, Guesses for those rare 
individuals with all three bad sleep attributes (SD = 1, Badtime = 1, and TSleepy = 1, n 
= 12) are significantly farther from equilibrium compared to subjects having all three 
good sleep attributes (SD = 0, Badtime = 0, and TSleepy = 0). As bad sleep conditions 
accumulate from the double- to triple-bad condition, the magnitude of the behavioral 
effect grows as well.5 Thus, our key result is that subjects with more adverse sleep 
attributes submit guesses consistent with lower levels of iterative reasoning, even in a 
largely uncontrolled experimental environment. 
 
 
 
4. Conclusions 
 
How sleep choices and time of day affect higher level thinking is of particular 
importance in modern societies that seem to continually constrain individuals to perform 
under adverse sleep and time-of-day conditions. Our results show that responses in the 
Guessing Game are farther from equilibrium if one slept less than 6 h the previous night 
(compared to more than 7 h) or if several adverse sleep attributes are present. While 
non-equilibrium responses in this Guessing Game may result from bounded rationality 
or expectations that others are not rational, more recent research on 2-person Guessing 
Games concludes that even when the influence of expectations is removed, rationality 
is still bounded (Grosskopf and Nagel, 2008). Thus, a reasonable interpretation of our 
results is that sleep loss harms this type of rationality (i.e., iterative reasoning and 
anticipation). Moreover, we find that a cocktail of several adverse sleep states magnifies 
the extent of this effect. So while a middle-of-the night decision may not, by itself, 
significantly affect behavior, when added to one already prone to sleepiness or with little 
sleep the previous night (or both), the effects on higher level thinking are shown to 
accumulate. 
 
 
Acknowledgements 
 
The authors wish to thank Mike McKee for helpful comments on this manuscript. We 
also thank the Appalachian State University for providing funding for this research. 
 
 
 
 
 
References 
 
Dickinson and McElroy, 2009 D.L. Dickinson and T. McElroy, Naturally-occurring sleep 
choice and time of day effects on p-beauty contest outcomes, Working paper, 
Appalachian State University #09-03 (2009). 
 
Grosskopf and Nagel, 2008 B. Grosskopf and R. Nagel, The two-person beauty contest, 
Games and Economic Behavior 62 (2008), pp. 93–99.  
 
Johns, 1991 M.W. Johns, A new method for measuring daytime sleepiness: the 
Epworth sleepiness scale., Sleep 14 (6) (1991), pp. 540–545.  
 
Nagel, 1995 R. Nagel, Unraveling in guessing games: an experimental study, American 
Economic Review 85 (5) (1995), pp. 1313–1326. 
 
Smith et al., 2002 C.S. Smith, S. Folkard, R.A. Schmieder, L.F. Parra, E. Spelten and H. 
Almirall et al., Investigation of morning–evening orientation in six countries using the 
preferences scale, Personality and Individual Differences 32 (2002), pp. 949–968.  
 
Stoller, 1997 M.K. Stoller, The socio-economics of insomnia: the materials and 
methods, European Psychiatry 12 (Suppl 1) (1997), pp. 41s–482s. 
 
 
Notes 
1 Based on National Sleep Foundation survey data. These survey data report average 
nightly sleep levels that are consistent with the authors' objectively measured average 
nightly sleep levels (see Dickinson and McElroy, 2009). 
 
2 An alternative is to define TSleepy based on splitting the sample at mean response = 
8, which produces qualitatively similar results. Trait-level sleepiness questions in the 
survey are from the well-known Epworth Sleepiness Scale (Johns, 1991), which is 
comprised of 8 questions/scenarios. We inadvertently omitted one of the scenarios in 
our question set, leaving us with 7 scenarios. 
 
3 Online Appendix available at 
http://www.appstate.edu/~dickinsondl/pdfs/EL28502_APPENDIX.pdf , which also 
includes the email text used for recruitment. 
 
4 This analysis, which is akin to split-sample analysis, is different than analyzing Guess 
for the interaction variables = 0 v. = 1 (where the interaction may equal 0 if either 
dummy variable equals zero). These key results remain unchanged if one uses dummy 
variable interaction terms instead. 
 
5 Combined conditions are also a useful way to combat the subject response error likely 
present in TSleepy and SD. 


Rationality around the clock: Sleep and time-of-day effect on guessing game responses

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Rationality around the clock: Sleep and time-of-day effect on guessing game responses

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