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“Sleep choice and circadian mismatch affects strategic reasoning.”
David L. Dickinson Dept. of Economics Appalachian State University
Boone, NC. 28608
828-262-7652 (phone): dickinsondl@appstate.edu Todd McElroy
Dept. of Psychology Appalachian State University
CLASSIFICATION:
Economic Science
Psychological and Cognitive Science
1 ABSTRACT
The ability to strategically reason is important many competitive environments. Trait-level cognitive skills have been shown to affect strategic behavior, but important temporal variations in state-level cognition are not uncommon. A common source of state-level cognition variability is sleepiness, which may result from sleep loss or circadian timing. We examine ecologically valid sleep and circadian effects on strategic reasoning, using a task that engages controlled thought areas of the medial prefrontal cortex (1) associated with mentalizing. Our first result is that that voluntary sleep loss, as well as relatively mild circadian mismatch, harms subjects’
strategic reasoning. However, a second results is that choice evolution during repeated play is
resilient, which is consistent with the hypothesis that automatic thought is more resilient to
cognitive resource depletion than controlled thought processes (2). These results demonstrate
that even relatively mild levels of voluntary sleep loss, as well as adverse (but not extreme) times
of day, can produce decrements in strategic reasoning that may harm successful adaptation to
new competitive environments. Further analysis of our data also reveals evidence that higher-
than-average levels of sleep harm strategic reasoning similar to low sleep levels, indicating that
strategic reasoning is not monotonically improving in one’s level of sleep. These results suggest
that current trends in sleep habits and scheduling may be maladaptive and lead to suboptimal
choices in decision environments where anticipation is important, such as in financial markets,
driving commute choice, and threat assessment.
2 Many strategic decision environments require the ability to anticipate others’ actions in order to succeed or survive. Not surprisingly, the laboratory experiment interest in p-beauty contest games (henceforth, “Beauty Contest”) stems from a desire to understand strategic reasoning in such environments (3). John Maynard Keynes (4) considered newspaper
competitions where entrants were asked to pick out the six most “pretty” faces (from a series of photographs), and a prize went to the person whose pick corresponded most closely with the average preferences of all respondents. A Beauty Contest game, in general, is straightforward.
Subjects in a group are asked to submit a number X from a designated interval X=[x
min, x
max], and let be the average of all guesses. The guess closest to p* times the average guess wins a prize, where p>0 is a common knowledge parameter. Variations in the Beauty Contest
environment are made by altering the parameter p. For p=1, pure coordination is rewarded, such as with the Keynes’ newspaper competition, whereas 0 < p ≠ 1 captures an environment where success depends on one’s choice deviating from the group average in a specified way. For example, Ho et al. (5) describe stock market behavior (also suggested by Keynes) as a Beauty Contest where p < 1 in the sense that selling a rising stock before others yields the highest payoff. Threat assessment also requires this type of strategic reasoning (i.e., mentalizing as to others’ intentions or actions), as do more mundane decision arenas such as one’s choice of morning commute route in a congested city.
Thus, the Beauty Contest captures many important features of strategic reasoning that are building blocks for decision making outside the lab. Recent research documents neural
correlates of Beauty Contest decisions in the medial prefrontal cortex (1), which has been
implicated in choices related to mentalizing (6-11). Behavioral researchers have evaluated such
games experimentally (3, 12-17), and a general conclusion is that individuals are strategic but do
not possess the infinite depths of rationality assumed in theory. Rather, results are consistent
with the hypothesis of bounded rationality, meaning one’s ability to anticipate is finite and it
differs across individuals. A key determinant of the between-subject heterogeneity in such
strategic reasoning abilities appears to be one’s trait-level cognitive skills (18). However,
because one’s state-level cognition can exhibit temporal variation, our study helps fill an
important gap in our understanding of cognition and reasoning.
3 In particular, we consider adverse sleep states—sleep deprivation and off-peak times-of- day—as a pervasive modern societal example of temporal variation in the cognitive resources one may bring to bear on a decision. We implement an ecologically valid protocol of voluntary sleep choice and circadian mismatch (i.e., performance at one’s suboptimal time of day) on 102 subjects to explore the hypothesis that even voluntary sleep loss and relatively mild circadian mismatch of the type experienced by real world decision makers can harm one’s ability to strategically reason in a new environment. We also administer the Beauty Contest repeatedly with full information feedback on others’ decisions in the previous round. In doing so, we are able to examine whether adverse sleep states affect one’s ability to adapt their decisions. In this full-information feedback environment, such adaptation implies engagement of more automatic thought processes (i.e., mimicking others’ choices, see (19)) than when the Beauty Contest is first administered. Thus, the particular Beauty Contest experiment we use allows us to explore the effects of sleep loss and circadian mismatch on both strategic reasoning (i.e., a controlled thought process) and on more automatic response processes. This is an important distinction given that psychologists have suggested that automatic thought processes are less affected by cognitive resources depletion than controlled thought processes (2,20). In other words, certain decision domains may be less susceptible to temporal variations in cognition, or perhaps
automatic response mechanisms may dominate a decision outcome that might normally involve more conscious deliberation.
Our study is highly relevant in a world where most individuals fall prey to modern
scheduling demands. The average American adult now sleeps less than 7 hours per night, the
percentage of adults sleeping less than 6 hours per night has risen steadily and significantly in
recent years, and there is mounting concern that as many as 50 million American adults are
chronically sleep deprived (see www.sleepfoundation.org). Recent data from the Bureau of
Labor Statistics also show that over 21 million wage and salary workers (approximately 18%)
performed some type of shift work, with disproportionally larger percentages of shift work
performance in safety-sensitive occupations such as health care support (27.9%), protective
service workers (50.4%--includes police and firefighters), and transportation/material moving
(29%) (21). Though our study focuses on sleep loss and circadian mismatch as the cause of
depleted cognitive resources, we believe it sheds important light on the more hidden decision
4 consequences of temporal variations in state-level cognition, in general. And, because strategic reasoning is important for success in competitive environments, those less able to anticipate others’ actions are at greatest risk of failure.
Sleep Effects on Cognition and Decisions
The homeostatic drive for sleep increases as a function of accumulated wake time.
Reduced cognitive performance (22,23), increased accident rates (24,25), and increased decision error (26,27) have all been attributed to sleep loss. Superimposed upon this homeostatic process is the circadian rhythm, which is responsible for the daily cyclical variation in sleepiness and alertness that differs across individuals. An evening-type individual (a.k.a., an “owl”) is
typically quite sleepy at 8 a.m., while this is a point of relative alertness for a true morning-type individual (a “lark”). Researchers have found decreased performance due to circadian mismatch (i.e., performance at one’s non-preferred time-of-day) in the areas of recall memory, subjective alertness, visual attention, and reaction times (28,29). Others have shown predictable
performance dips among shift workers (30) and driver safety (24) at times that correspond to circadian off-peak times-of-day.
However, only recently has sleep research begun to look more explicitly at the higher- level decision effects of sleep deprivation (31). Higher-level “controlled” thought processes are concentrated in the prefrontal cortex (PFC) brain region, which is known to be affected by sleep loss (32). Nevertheless, research has not always produced a consistent theme as to how sleep deprivation affects PFC activation. Some have found that compensatory cerebral recruitment can occur following acute total sleep deprivation of 35 hours, thus helping maintain performance outcomes (33). However, others have shown behavioral responses following such sleep
deprivation in a different high-level task (34) to be similar to that of individuals with prefrontal
lesions performing a similar task (35). As a result, general conclusions about sleep or circadian
effects on decision-making are challenging, perhaps highlighting the need to more carefully
consider task attributes. For example, psychological research has shown that cognitive resource
depletion, such as we hypothesize would result from sleep loss or circadian mismatch, may lead
to increased reliance on automatic response habits that are typically regulated by controlled
thought processes (36-38). This research also shows that deliberate or effortful thought relies on
5 more consciously-controlled processing (2,39-40). Thus, our working hypotheses is that sleep loss or circadian mismatch will reduce one’s engagement of controlled thought processes in favor of more automatic thought processes in decision-making.
Strategic reasoning in the Beauty Contest
The Beauty Contest is a game where strategic reasoning improves one’s outcome and chances for success. In our parameterization, subjects choose an integer in the [0,100] interval, and the guess closest to p=.7 times the average guess wins a monetary prize (approximately $7 per decision round). When subjects first play this game, they have no feedback on others’
choices, and so high-level reasoning is engaged. In particular, the predicted equilibrium guess of zero is only reached by infinite elimination of dominated strategies. For example, if p=.7, then guesses in the [70,100] are rationally eliminated given the maximum possible target guess is p*100=70. If guess are thought to then be in the [0,70] interval, the rational player further eliminates guesses higher than p*70, and so on. Though the game’s simple prediction also assumes that everyone assumes everyone else is rational, guesses that deviate from equilibrium are typically used as evidence of some cognitive limit to rationality (3). Experimental research has produced results showing finite reasoning consistent with a cognitive hierarchy model (1,3,5,15). Additional supporting evidence of limits to cognition is found in two-person Beauty Contest games where most choices involve dominated strategies (13).
Though uninformed play of this game is a novel task that engages high-level executive
thought processes typical of the PFC, repeated play of the game should, by definition, lead the
task to become automatic (42). If the task is repeated with full information feedback on previous
round outcomes, subjects can rather simply adapt their responses to mimic winning responses
(i.e., a more automatic response mechanism). Evidence from psychology suggests that well-
learned tasks that require little thought will rely more on automatic response mechanisms or
unconscious processing (39,41,42-45), such as we suggest is the case during repeated play of the
Beauty Contest with feedback. Thus, uninformed initial guesses are hypothesized to display
more limited strategic reasoning, implying responses further from the rational equilibrium
prediction, for circadian mismatched or voluntarily sleep deprived subjects. However,
6 adaptation during repeated play is hypothesized to be more resilient to these temporal declines in cognition.
RESULTS
Voluntary Sleep Loss and Circadian Mismatch Results
Results are from a p=.7, X∈[0 , 100], which generates and equilibrium prediction of X=0 for infinitely strategic subjects (46). We subjectively define sleep-deprived (SD) as “less than 6.5 hours of nightly sleep” for the week prior to the decision task—our sample is then 55% SD subjects, 45% WR (well-rested) subjects. Round 1 decisions (or “guesses”), display significantly lower levels of strategic reasoning for the SD group compared to the WR group, with Guess
SD= 60.15 > Guess
WR= 48.36 [p=.02, Mann-Whitney, one-tailed test]. Circadian mismatch (MM) is randomly allocated across our subject pool of morning-type and evening-type subjects.
Mismatch implies either a morning-type subject in an 8 p.m. experiment session or an evening- type subject in an 8 a.m. session. Subjects at their less adverse time-of-day are considered circadian matched (CM). Our results show that circadian mismatch produces similar decrements in strategic reasoning compared to voluntary sleep loss. Round 1 guesses for MM subjects are farther from the rational equilibrium prediction than guesses of circadian matched, with Guess
MM= 61.15 > Guess
CM= 48.01 [p=.02, Mann-Whitney, one-tailed test]. If we examine this result by circadian mismatch subgroup, we find that initial guesses do not differ in the morning session comparing matched morning-type and mismatched evening-type subjects
[Guess
MM,8am=57.15≈58.63=Guess
CM,8am, p>.10, Mann-Whitney 2-tailed test]. In other words, evening-type subjects at 8 a.m.—a circadian mismatch—strategically reason similar to morning- type subjects at 8 a.m.—a circadian match.
The circadian mismatch result is predominantly due to evening session decisions being significantly more strategic among evening-type subjects
[Guess
MM,8pm=65.31>37.81=Guess
CM,8pm, p=.00, Mann-Whitney 2-tailed test]. This result is perhaps counter-intuitive given that morning-types are still typically awake at 8 p.m. (compared to evening-types at 8 a.m. in the morning). It is also the case that evening-types give responses at their optimal time of day that are significantly closer to equilibrium than responses of
morning-types at their optimal time of day [Guess
CM,8pm=37.81< Guess
CM,8am=58.63, p=.01,
7 Mann-Whitney 2-tailed test]. Thus, evening-types may simply be better at strategic reasoning or mentalizing at 8 p.m. compared to morning-types at 8 a.m. The established morning and evening time slots in our protocol correspond to roughly equal levels of expected alertness for circadian matched subjects (47), but objective behavioral responses are apparently mediated by other considerations specific to diurnal preference. Future research will be needed to further explore this particular finding.
Though strategic reasoning is affected by temporal fluctuations in cognition produced by sleep and circadian variation, our second result highlights that not all thought processes will display similar effects. Summary results in Fig. 1 reveal that the typical convergence towards equilibrium following initial round choices is appears largely unaffected by sleep or circadian state variation. This is confirmed by analysis of a simple qualitative learning model that assumes a rational response to a losing guess in the previous round would be to modify one’s current round response in the direction that would have placed one’s guess closer to the target (3). Thus, we find that adjustment to a losing guess in the previous round is not affected by the same
temporal cognition change that affected strategic reasoning. Fig. 2a and 2b visually highlight that guess adjustment does not differ between sleep and circadian subgroups and that, on average, guesses adapt in the rational direction as evidenced by the positive slope of the scatter plots (see online Supporting Information for specifics of subject learning analysis). Given the full information feedback environment of our decision experiment, this supports our conclusion that more automatic response mechanisms can be resilient to cognitive resource depletion, even though controlled thought processes that depend more on the integrity of the prefrontal cortex may be harmed.
Predicting strategic reasoning
The actigraphy data are continuous and thus allow us to estimate a behavioral model of strategic reasoning as a function of the continuous nightly sleep quantity, SleepQ. We also create a mismatch scale variable, MMscale, to score mismatch in the [0,1] interval that reflect the degree of circadian mismatch (e.g., the most extreme evening-type in the morning session is more mismatched than a mild evening-type in the same session).
Consider the following model of initial round guesses for the i
thsubject (N=102):
8 Guessi = α + β
1*Female +β
2*NFC +
β
3*SleepQ
i + β
4*SleepQ
i2 + β
5*MMscale
i + β
6*MMscale
i2 + ε. [1]
Controls are included for two main subject-specific variables: gender and Need for Cognition (NFC) score. The NFC score measures one’s preference to engage in and enjoy thinking, and it does not interact with subject gender (48). We use the NFC measure as a rough proxy for a subject’s state-level cognitive skills. Key coefficient estimates of β
3, β
4,β
5are statistically significant at the .01 level (β
6estimate significant at the .05 level). Gender is not a predictor of strategic reasoning, although one’s NFC score does predict strategic reasoning in the expected direction. Thus, though we find some evidence that preferences towards reasoning (i.e., higher NFC score) lead to more strategic decisions in the Beauty Contest, we find a highly significant effect of the state-level sleep quantity and circadian variables on strategic reasoning.
Estimates from [1] produce the forecast Guess shown in Fig. 3, which shows nonlinear effects of sleep quantity on strategic reasoning, holding other variables constant at mean levels.
We include the unconditional average data in Fig. 3 as well, which confirm that this U-shaped profile is robust. These estimates forecast that strategic reasoning in the Beauty Contest is optimized (i.e., guesses closest to rational equilibrium) at nightly sleep of just under 7 hours. As a function of degree of circadian mismatch, the estimates from equation [1] predict that, while strategic reasoning is forecast to be optimized at mismatch level of zero, intermediate mismatch levels may be worse than extreme mismatch for subject reasoning. This is consistent with our earlier (counter-intuitive) result that showed how more apparently severe mismatch need not lead to behaviorally inferior outcomes, though we only speculated as to why. We note, however, that our continuous mismatch scale variable lacks the precision of our sleep quantity variable, and so we place less emphasis circadian mismatch forecast from equation [1] (49).
The estimated U-shaped behavioral effect of nightly sleep duration on anticipatory
thought in the Beauty Contest is particularly interesting given extant sleep research showing
increased mortality rates among “long-sleepers” as well as short-sleepers (50). Such study
results include current longitudinal studies (51,52), though there still remains questions as to
confounds in using such population studies to make causal inferences (53,54). We simply note
that our data offer a unique behavioral twist to the possibility that both sleep restriction and
extended sleep may cause decrements in important outcome variables.
9 Finally, the estimates from equation [1] can also be used to make and out-of-sample forecasts for the hypothetical decision maker at the estimated worst points in terms of voluntary sleep and circadian mismatch. The forecast for nightly average sleep of 5 hours per night and circadian mismatch level=.65 (the estimated worst mismatch level from equation [1] estimates) is a guess=78. This contrasts with the forecast guess=23 for 7 hours sleep per night with low circadian mismatch level=.05. This amounts to a difference of multiple stages of strategic reasoning, which is behaviorally quite significant in magnitude. Such a difference would be found between an individual who essentially guesses at random and one who can anticipate what others will choose, while assuming also that others will anticipate that others are similarly strategic. These results are not meant to imply that outcomes on this or similar tasks would produce similar results under more extreme adverse sleep conditions. Nevertheless, these results are of significance given their high external validity for real-world decision makers in our
ecologically valid study design. Sleep loss is sometimes considered a badge of honor in modern society, but our results indicate that the biological need for sleep is forsaken at a behavioral cost.
Discussion
Temporal variations in cognition may arise for numerous reasons. We hypothesized that state-level sleep and circadian variations alter available cognitive resources, though there may exist other cognition risk factors worth exploring. For example, both amount of time
deliberating and distractions during decision-making are routinely used as tools for manipulating the availability of cognitive resources and consequential effects on choice preferences in
behavioral psychology research (55,56) A useful analogy for our hypothesis of cognition effects on strategic reasoning is to consider how outcomes on a performance task are determined at the trait-level by one’s abilities, but at the state-level by one’s effort on the task. Similarly, we have suggested that naturally-occurring sleep loss and circadian mismatch produce temporal variations in cognition independent of one’s trait-level cognitive skills.
It is well known that acute total sleep deprivation causes decrements in prefrontal cortex
(PFC) driven tasks (32), and more limited evidence suggestions that time of day modulates
cognition in certain aspects of high-level decision-making (57). Our research is an attempt to
explore the boundary conditions of PFC deficit on behavioral outcomes. We hypothesize that
10 adverse (but relatively mild) sleep and circadian challenges more typical of naturally occurring decision environments may still cause deficits in PFC functioning sufficient to alter PFC-driven strategic reasoning. Strategic reasoning in the Beauty Contest has been shown to correlate with neural activity in the medial PFC (1), and so our task selection allows an appropriate test of our hypothesis.
Individuals may be overconfident with respect to their own behavioral susceptibility to adverse sleep states, especially when able to utilize countermeasures (e.g., effort, caffeine, etc).
However, previous research is pertinent with respect to self-perceptions of sleepiness. Evidence has shown that chronic but partial sleep loss affects subjective sleepiness significantly less than does acute total sleep loss, though chronic partial sleep loss still produces significant deficits in some measures of cognitive performance (58). Also, physiological manifestation of one’s sleepiness may not appear until an individual is (subjectively) extremely sleepy (59). Thus, ecologically valid environments may not be conducive towards recognition of some states of weakened cognition. This may be particularly true if critical outcomes measures within the environment are isolated to decision effects, as opposed to more readily apparent effects on other cognitive functions such as reaction time, speech acuity, or motor function.
Our secondary result is that the adaptation response process resulting from repeated administration of the decision task was resilient to voluntary sleep loss and mild circadian mismatch. Future research will have to examine at what point more severe challenges to temporal cognition would alter this result (e.g., extended total sleep deprivation). Our data are consistent with a dual systems framework of cerebral function that includes both controlled thought and automatic/unconscious response systems (60,61). While the temporal deficit in cognition caused by sleep loss and circadian mismatch significantly lowers strategic reasoning, the less PFC-driven process of adaption was unaffected by these same temporal cognition deficits. This may suggest that some decision arenas are not at risk to certain commonplace variations in cognition. However, it may not be generally optimal that one system remain intact without the other’s usual input—consider, for example, regulation of emotional responses.
Disequilibrium between automatic and controlled thought processes due to cognitive stress of any type may therefore lead to decisions that are suboptimal, socially inappropriate, or irrational.
If we confine ourselves just to the realm of strategic decision environments, it is clear that
11 weakened anticipation skills puts one at a competitive disadvantage in many decision arenas where reasoning and anticipation are important.
METHODS
Subjects. A total of 102 (46 females) were recruited to participate in an experiment that consisted of two sessions, set one week apart, and both at a common randomly assigned morning (8 a.m.) or evening (8 p.m.) time of day. The subjects were recruited from a database of several hundred subjects who had completed a short sleep survey. Exclusion criterion included: self-reported diagnosed sleep disorder, objectively scored risk for major depressive or anxiety disorder (as ascertained from validated questions on the sleep survey). The sleep survey also included a validated diurnal preference survey instrument (62)—the validated instrument was a reduced form of the classic morningness-eveningness survey instrument in Horne and Ostberg (63). This instrument, henceforth rMEQ, characterizes respondents as follows: 4-11 Evening types, 12-17 Intermediate types, 18-25 Morning types. Due to the rarity of true morning types (less than 10% in similar young adult populations (64)), we recruited some subjects with rMEQ scores 16 and 17. We therefore mostly eliminated intermediate-types from consideration, with the main objective of a clear rMEQ score separation between groups. From this database of eligible
morning-type (MT) and evening-type (ET) subjects, all are ex ante randomly assigned to a morning or evening experiment session, and then recruited for the main experiment phase. In this way, individuals could choose to not respond to the recruitment message, but they could not self-select into the alternative time slot by declining their randomly assigned session time slot. Table 1 shows relevant demographic and sleep statistics on the study subjects within each treatment cell of the 2x2 circadian match/mismatch manipulation.
Experiment Sessions. The two sessions of the main experiment phase were as follows: Session 1 could
be on a Tuesday, Wednesday, or Thursday (morning or evening session). Session 2 was the following
week on the same day of the week as Session 1 (i.e., 7 days later). Midweek days were used to avoid
weekend sleep effects on decisions. In Session 1 subjects gave voluntary informed consent to participate
in the study, completed 3 short survey instruments (including the Need for Cognition instrument used as a
control for estimating equation [1]), and were given instructions on the use of a wrist-worn actigraphy
device and complementary sleep diaries. Subjects then return one week later for Session 2 having worn
the actigraphy for the week and kept sleep journals. Importantly, subjects were instructed to carry out
their typical sleep routine, such that our sleep quantity is both objective and ecologically valid. At the
12 time of decision-making during Session 2, we therefore have an objective measure of sleep during the week leading up to the administration of the decision experiment.
Sleep data acquisition
The actigraphy devices used are accelerometers with sensitivity of .05 g-force, worn on the non-dominant wrist to measure its activity as a proxy for gross motor activity (model AW-64, Phillips Respironics).
Data sampling is at epoch lengths of 30-seconds. The devices are impact resistant, water-proof to 1-meter depth for 30 minutes, and can therefore be worn 24-hours a day with few exceptions. The actigraphy data were scored using the manufacturer’s software which, along with complementary sleep diary data, generates an objective and validated measure of total sleep time that does not significantly differ from polysomnography-derived measure (see (65) and references therein). In our sample, nightly sleep
average between the morning- and evening-types is not significantly different [Mann-Whitney test, p>.10, two-tail test], indicating no confounding correlation between diurnal preference and sleep levels.
Beauty Contest task design
Two parameterizations of the Guessing Game are administered following Ho et al. (5), and we report here the more cognitively challenging p<1 treatment. A second treatment used p=1.3, and guess interval [100,200]. Full details and analysis on treatment 2 data are in the online supporting information appendix, and the treatment 2 results support our treatment 1 conclusions. We consider treatment 2 less cognitively challenging, and therefore a less sharp test of our main hypothesis with respect to temporal cognition effects, because the equilibrium guess of 200 is reached at a finite level of reasoning.
Treatment 1 parameters require infinite depth of strategic reasoning to reach the equilibrium prediction of zero for that treatment. Both treatment 1 and 2 were administered as a block of 10 rounds with full information feedback for a total of 20 decision rounds per experiment. In different sessions, subjects were first administered treatment 1, whereas in others they were first administered treatment 2. Initial round analysis of the data examines the first round of the treatment, which could be round 1 or 11.
Because round 11 involves an already learned task, but yet with new parameters, we consider separate estimation of equation [1] for round 1 versus round 11 decisions. For our treatment 1 data, the key sleep quantity nonlinear effect remains significant, although the circadian mismatch effect does not. Thus, the mismatch result is less robust than the sleep quantity result, consistent also with the data on the
cognitively less challenging treatment 2 (Table S1, SI appendix).
Payments
13 All subject were compensated a flat payment of $30 for the 7 days of actigraphy and sleep diary data.
Subjects were financially motivated in each round of their Beauty Contest decisions—a prize was given for the winning guess (i.e., the guess closest to p=.7 times the average guess), and in the event of a tie, but prize was equally shared among the winners for that round. Payoffs averaged a total of $52.55 for each subject: $30 for the actigraphy and sleep diary data, and then $22.55 ± $8.84 from the Beauty Contest decisions.
Acknowledgments
The authors thank Clare Anderson for helpful comments, as well as seminar participants at the University of Arizona (Institute for Behavioral Economics), University of Calgary (Psychology), George Mason University, Emory University, GATE economics research institute, the
University of Luxembourg (Law, Economics and Finance) and Appalachian State University.
Research was funded by Appalachian State University (Research Development Award). Finally,
we thank Valerie Sanchez, Andrew Hunt, Myra Miller, Katie Lambert, and Holt Menzies for
valuable research assistance.
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18 Time Session for Decision Experiment
Summary statistics (N, averages, standard deviations) Chronotype 8:00 a.m. (morning) 8:00 p.m. (evening)
Morning type
N=24 (15 female) Age=23.9 ± 9.4 years old Avg. MEQ score= 17.42 ± 1.5 Avg. nightly sleep=374 ± 65 min Avg. wake time=8:12 a.m. ± 73 min Avg. bed time=12:21 a.m. ± 73 min Avg. sleep efficiency*=82% ± 5.0%
N=26 (5 female) Age=26.9 ± 12.1 years old Avg. MEQ score=18.07 ± 1.8 Avg. nightly sleep=379±61 min Avg. wake time=7:37 a.m. ± 60 min
Avg. bed time=12:03 a.m. ± 77 min Avg. sleep efficiency*=80%±6.7%
Evening type
N=27 (10 female) Age=20.7 ± 2.5 years old Avg. MEQ score=7.15 ± 2.2 Avg. nightly sleep=389 ± 49 min Avg. wake time=10:04 a.m. ± 72 min
Avg. bed time=1:46 a.m. ± 66 min Avg. sleep efficiency*=81% ± 7.1%
N=25 (16 female) Age=21.4 ± 5.4 years old Avg. MEQ score=6.56 ± 1.32 Avg. nightly sleep=380 ± 64 min Avg. wake time=9:59 a.m. ± 94 min
Avg. bed time=2:03 a.m. ± 61 min Avg. sleep efficiency*=84% ± 4.8%
Table 1. Chronotype and Time Session assignments. In the text, circadian mismatch is used to refer to both morning-type subjects in evening experiment sessions and evening-type subjects in morning experiment sessions. Otherwise, we refer to subjects as circadian matched in the text.
*Sleep efficiency is the percentage of the time within the subjects nightly attempted sleep intervals that is scored as actual sleep. That is, sleep efficiency takes into the time taken to fall asleep as well as any bouts of wakefulness during the night as measured by the actigraphy.
Note: ± indicates standard deviation.
19 Fig. 1. Average guess by decision round within treatment.
SD=sleep deprived, WR=well-rested
MM=Circadian mismatch, CM=circadian match Data pooled across individuals by sleep state.
Predicted guess for infinitely rational subject is guess=0.
Fig. 2a Response sensitivity to previous round outcome by sleep state (SD or WR, OLS prediction overlaid)
Fig. 2b Response sensitivity to previous round outcome
By circadian state (CM or MM, OLS prediction overlaid)
20 Fig. 3: Forecast guess by sleep level
Fig. 4. Actigraphy data from one 24-hour period of experiment protocol (Thursday noon through Friday noon), sampled at 30-second time epochs.
Morning-types (n=50) shown in green, evening-types (n=52) shown in red.
21 Supporting online information APPENDIX
Circadian profile of sample
Our subject pool is divided into two groupings of rMEQ score, which we identify as morning- and evening-types. Though our cutoff rMEQ score for morning-types is slightly different from standard cutoffs, we maintain a clear separation of rMEQ scores in our groups.
Fig. S1 shows the frequency of each rMEQ score for our sample, along with traditional cutoff points for classification as morning-, intermediate-, and evening-types.
Forecast predictions analysis
The forecast nonlinear effects discussed in the main text are based on the coefficient estimates shown in Table S1. The model estimated is
Guess
i= α + β
1*Female +β
2*NFC +
β
3*SleepQ
i+ β
4*SleepQ
i2+ β
5*MMscale
i+ β
6*MMscale
i2+ ε. [1]
Estimation is by simple ordinary least squares model of one’s initial round guess, which are treated as independent observations. The mismatch scale variable, MMscale, is defined as:
Thus, MMscale generates mismatch values in the [0,1] range. As noted in the main text, inclusion of group specific fixed effects does not alter our results. The estimated nonlinear effects are similar for both treatments in that guesses closest to equilibrium are predicted at around 6.75-7.0 hrs sleep per night, and a medium-high level of circadian mismatch is estimated to generate guesses farther from equilibrium than more extreme mismatch levels.
Treatment 2 data
We administer a second treatment of the Guessing Game with parameterization p=1.3,
and guess interval=[100,200] (1). This Treatment 2 differs cognitively from Treatment 1 in that
the equilibrium rational guess is the upper bound of the guess interval, 200. Additionally, if
22 anticipation is considered to proceed by an iterative process, then one reaches equilibrium with a finite number of reasoning stages. For example, even if all subjects guessed 100, then
1.3*100=130 would be the target guess. If one assumes other subjects reason to this extent, then the average guess would actually be 130, such that the target guess is now 1.3*130=169. One more stage of reasoning (or beyond) leads all subjects to submit the maximal guess of 200. We therefore consider Treatment 2 cognitively more simple than Treatment 1, and less likely to display the hypothesized behavioral effects of voluntary sleep loss and circadian mismatch.
Subjects were administered 10 rounds of each treatment, with half the groups administered Treatment 1 first, and the other half Treatment 2 first.
Results from Treatment 2 are qualitatively similar to Treatment 1 results with respect to sleep deprivation. Initial guess in Treatment 2are significantly farther from the rational
equilibrium for the voluntary sleep loss group, Guess
SD= 150.80 < Guess
WR= 160.62 [p=.03, Mann-Whitney, one-tailed]. However, circadian mismatch does not significantly affect initial guesses in Treatment 2: Guess
MM= 152.25 ≈ Guess
CM= 157.98 [p>.10, Mann-Whitney, one- tailed]. A nonlinear nightly sleep time effect in Treatment 2 is also estimated similar to the nonlinear effect in Treatment 1. A simple least squares estimate of equation [1] for Treatment 2 produces a forecast that one’s anticipatory thought is optimized (i.e., closest to equilibrium) at about 7 hrs sleep per night, holding constant the level of circadian mismatch (see Table S1).
Learning and Adaptation
An overview of the pattern of treatment 2 guesses across all 10 rounds is in Fig. S2.
Convergence to equilibrium is qualitatively similar to the treatment 1. Following Nagel (2), we
can more specifically examine the data’s conformity to a qualitative learning model that assumes
subjects adjust their guess in the direction of (ex post) the optimal adjustment factor: the
23 learning-direction theory. Nagel (2) defines subject i’s adjustment factor and the optimal
adjustment factor as
[2]
[3]
where (mean)
t-1is set equal to the midpoint of the guess interval for the first round of the treatment. A “good” adjustment, as defined by this qualitative learning model, is one where a subject changes her adjustment factor to correct the direction of the previous round’s error. That is, if a
t> a
opt, tthen a
t+1< a
trepresents a good adjustment (and a
t< a
opt, timplies a
t+1> a
t).
Analysis is restricted to the subsample of the data where the subject did not win or share in the prize in the previous round, as such rounds present subjects with distinct feedback. By doing so, we have a sample of N=787 treatment 1 and N=297 Treatment 2 guesses in response to a no-win outcome in the previous round.
We find that in the pooled data 75% of subject guesses in Treatment 1 are consistent with learning-direction theory, similar to proportions reported in Nagel (2). In Treatment 2, the proportion is just 56%, though this is still statistically different from random adjustment factor alterations based on a coin flip [binomial test: p=.03, one-sided test against the null hypothesis that the probability of a guess consistent with learning-direction is 50%]. Table S2 shows the results of evaluating the learning-direction theory compared to a more naïve rule-of-thumb adjustment process by which subjects just continue to adjust their guess in the direction of the predicted equilibrium, independent of what the winning guess was in the previous round,
equilibrium guess adjustment. For the most part, there are no statistically significant differences between the proportion of guesses conforming to the learning-direction model across the
subsamples of sleep deprived versus well-rested, or circadian matched versus mismatched
subjects [two-sample proportions test: p-value >.10 in all cases]. A marginal result is that
learning-direction may be utilized more often in treatment 2 when a subject is well-rested
compared to sleep-deprived. While the result is statistically insignificant [p=.12] with the two-
sample proportion test, it is marginally significant [p=.09] using the binomial test. Alternatively,
by altering the subjective cutoff for coding SD=1 to a nightly average sleep of 6 hours or less
(instead of 6.5 hours or less), the result is significant using the two-sample proportions test
24 [p=.09]. Though not a robust result, this is suggestive that a further examination of learning effects should be on the agenda for future research. With respect to use of the naïve adjustment model, we also find no differences in use of either learning rule as a function of sleep or
circadian effects.
Finally, for a given sleep state (SD or WR, MM or CM) we examine whether a subject is more likely to use the more sophisticated learning-direction model or the naïve equilibrium guess adjustment model. In Treatment 1, we fail to reject the hypothesis that the proportion of guesses conforming to learning-direction is equal to the proportion conforming to equilibrium guess adjustment for SD or WR subjects [two-sample proportions test: p-value >.10]. We find the same result for Treatment 1 comparing the MM and CM subsamples. So, the various sleep sub- groups have no significant effect on the propensity to use one type of learning model versus the other. For Treatment 2, in all comparisons we find that subjects are more likely to use the naïve equilibrium guess adjustment model than the learning-direction model, which is not surprisingly the less complex decision environment of the two treatments. Though other learning models may be compared using our data, the purpose of our paper is not a comprehensive comparison of learning models. Most all learning models utilize some type of reinforcement learning based on previous round outcomes or payoffs. As such, Figures 1, 2a,and 2b (main text) seem to highlight what our simple analysis concludes—subject guesses seem to adjust in a rational way to
deviations from the target in the previous round, but this adjustment process does not appear to differ when a subject is sleep-deprived or circadian mismatched. These results are consistent with our hypothesis, which is based on the notion that adaptation in our experiments engages more automatic thought processes and should therefore be relatively unaffected by sleep state.
SI References
1) Ho T-H, Camerer C, Weigelt K (1998) Iterated dominance and iterated best response in experimental ‘p-beauty contests’. Amer Econ Rev, 88: 947-969.
2) Nagel R (1995) Unraveling in guessing games: An experimental study. Amer Econ Rev,
85: 1313-1326.
25 Variable Treatment 1 Treatment 2
Constant 401.97 (82.17)***
-29.78 (81.13) Female 8.40
(5.54)
-5.53 (5.47) NFC -.16
(.09)*
.05 (.09) Sleep
Quantity -1.92
(.44)*** .90
(.43)**
Sleep Quantity-
squared
.0024
(.00057)*** -.001 (.00056)*
Mismatch
Scale 114.85
(38.32)*** -45.77 (37.83) Mismatch
Scale-squared -87.40
(36.77)** 52.63 (36.30)
R
2.26 .15
Table S1. OLS estimation of initial round Guess (st. errors in parenthesis)
*,**,*** indicate significance at the .10, .05, and .01 levels, respectively, for the two-tailed test.
Learning-Direction SD=1 SD=0 MM=1 MM=0 Treatment 1 (N=787) 75% (N=422) 75% (N=365) 75% (N=412) 75% (N=375) Treatment 2 (N=297) 53% (N=176) 60% (N=121) 55% (N=164) 56% (N=133)
Equil. Guess Adj.
Treatment 1 (N=787) 73% (N=422) 72% (N=365) 71% (N=412) 74% (N=375) Treatment 2 (N=297) 80% (N=176) 83% (N=121) 80% (N=164) 83% (N=133)
Table S2. Summary of Learning Model Performance
Data analyzed is subset of data following a no-win choice round for the subject.
26
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
Frequency
MEQ score
4 8 12 16 20 25
evening‐types
morning‐types intermediate‐
types
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