Discussion Papers In Economics
And Business
An Experimental Study on Information Acquisition
and Disclosure in a Cournot Duopoly Market
Kazunori Miwa

Discussion Paper 13-01-Rev.

August 2021

Graduate School of Economics
Osaka University, Toyonaka, Osaka 560-0043, JAPANAn Experimental Study on Information Acquisition
and Disclosure in a Cournot Duopoly Market†
Kazunori Miwa‡

Abstract
This study experimentally investigates the interaction between ﬁrms’ information acquisition decisions and disclosure. In particular, I focus on a Cournot duopoly market underindustry-wide demand uncertainty. The results demonstrate that acquiring industry-wide
demand information improves ﬁrms’ production decisions in that ﬁrms can adjust theirquantity levels depending on the market demand. However, disclosure diminishes a ﬁrm’s
incentive to acquire such information. This is because once the information, which a ﬁrm
acquired at a cost, is subsequently disclosed, a rival ﬁrm can take a free ride on the disclosed
information and make a more informed decision. Hence, disclosure decreases the beneﬁtof acquiring information for the disclosing ﬁrm. Taken together, although acquiring information improves production decisions, disclosure decreases the incentive to do so and thus,
deteriorates a ﬁrm’s internal information environment. This leads to ineﬃcient production,
which in turn might have a substantial impact on market outcomes.

Keywords: Information acquisition; Disclosure; Duopoly; Experiment
JEL Classiﬁcation: L13; M41; M48†

The former title is “The Impact of Mandatory Disclosure on Information Acquisition: Theory and Experiment.”
Graduate School of Economics, Osaka University, 1-7 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
Email: miwa@econ.osaka-u.ac.jp
‡

1

1

Introduction

Numerous theoretical studies examine the interaction between information disclosure and product market competition and provide important insights on proprietary disclosures.1 Darrough(1993) analyzes a two-stage duopoly model. She demonstrates that when ﬁrms engage in Cournot
competition under industry-wide demand uncertainty, they would not commit to disclosing demand information because of its proprietary nature. Suijs and Wielhouwer (2014) extend Darrough’s (1993) model. They show that although Cournot duopolists prefer not to disclose demand information ex ante, mandatory disclosure requirements can enhance social welfare, especially when products are good substitutes. These suggest that disclosure regulation will besocially desirable in Cournot duopoly under demand uncertainty.2
I argue that it is unclear whether mandating disclosure can achieve the intended objective ofimproving social welfare when information acquisition is endogenous and costly. Of course, anantecedent of information disclosure is that ﬁrms must have acquired and possessed information
to disclose. Firms must often spend resources to obtain private information and thus face a tradeoﬀ between the cost and beneﬁt of information acquisition. In addition, if the acquired private
information is subsequently disclosed, not only the ﬁrm that acquired the information at a cost
but also its competitors can strategically use this information and make more informed decisions.
Therefore, mandatory disclosure potentially decreases the beneﬁts of acquiring information. In
this way, mandatory disclosure of proprietary information diminishes a ﬁrm’s incentive to acquire such information, and hence, its internal information environment deteriorates comparedto the case where disclosure regulation does not exist. This might lead to a substantial impact
on market outcomes.
The objective of this study is to experimentally investigate the interaction between ﬁrms’
information acquisition decisions and disclosure. The experiment is based on a simpliﬁed version of Miwa’s (2019) model. Miwa (2019) analyzes a Cournot duopoly model with stochastic
demand in which acquiring information is endogenous. I conduct a controlled experiment to test
the theoretical predictions derived from the model.
1See, for example, Vives (1984), Gal-Or (1985), Kirby (1988), Vives (1990), Darrough (1993), Sankar (1995),
Raith (1996), Clinch and Verrecchia (1997), Pae (2000), Pae (2002), Arya and Mittendorf (2007), Hughes andWilliams (2008), Arya, Frimor, and Mittendorf (2010), Bagnoli and Watts (2010), Corona and Nan (2013), Suijs
and Wielhower (2014), Bagnoli and Watts (2015), and Hughes and Pae (2015).
2
Most theoretical studies that analyze a stochastic oligopoly model consider two types of information, i.e.,
ﬁrm-speciﬁc cost information and industry-wide demand information. However, the key distinction is between
ﬁrm-speciﬁc and industry-wide information, not cost versus demand information (Christensen and Feltham 2003,
pp.544-545). In line with previous research, I interpret industry-wide information as demand-related.

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In the experiment, I manipulate the information acquisition cost (low versus high) in two
economic settings (disclosure versus nondisclosure). Hence, the experiment consists of four
treatments: disclosure and low cost (DL), nondisclosure and low cost (NL), disclosure and highcost (DH), and nondisclosure and high cost (NH). To simplify the setting, participants take therole of either a ﬁrm or a rival. Only the ﬁrm participants have a choice of whether or not toacquire information about unknown demand parameters at a cost. In nondisclosure conditions(i.e., treatments NL and NH), if a ﬁrm chooses to acquire information, it receives a perfect signal about the true demand state of the market before making a production decision. In contrast,
the paired rival does not receive any signals and remains uncertain about the market demand.
In disclosure conditions (i.e., treatments DL and DH), on the other hand, if a ﬁrm chooses toacquire information, both the ﬁrm and the paired rival receive a perfect signal. That is, demand
information that the ﬁrm acquired at a cost is disclosed to the rival. In this way, both the ﬁrm
and the rival learn the true demand state of the market before making their production decisions.
Regardless of whether the acquired information is disclosed or not, only a ﬁrm bears the information acquisition cost when it chooses to acquire information. The cost is either high or low,depending on the experimental treatments. If a ﬁrm chooses not to acquire information, boththe ﬁrm and the paired rival remain uncertain about the market demand in all treatments.
The main results are as follows. When ﬁrms learn the true demand state of the market throughinformation acquisition, they successfully adjust their production levels depending on the market demand. Speciﬁcally, if a ﬁrm acquires information and learns that the demand state is good(bad), it increases (decreases) its quantity level. When ﬁrms do not acquire information and remain uncertain about the market demand, they cannot adjust production levels depending on themarket demand. These indicate that acquiring demand information improves ﬁrms’ production
decisions.
However, the results show that if the demand information is disclosed to a rival, the rival canalso adjust its quantity level depending on the market demand. This means that disclosure allows
the rival to take a free ride on the paired ﬁrm’s costly information acquisition. In other words, if
a ﬁrm acquires information at a cost but must disclose it afterward, the beneﬁt of acquiring suchinformation is reduced. In fact, ﬁrms in nondisclosure conditions tend to acquire information
more frequently than those in disclosure conditions. This indicates that disclosure negatively
aﬀects ﬁrms’ information acquisition decisions. In addition, as expected, ﬁrms acquire information more frequently when the information acquisition cost is low.

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This study has several contributions to the literature. First, it contributes to the theoretical literature on information disclosure in an oligopoly market. Previous theoretical studies examine
how product market competition aﬀects ﬁrms’ disclosure decisions (e.g., Vives 1984; Gal-Or
1985; Darrough 1993; Sankar 1995; Raith 1996; Pae 2000; Arya and Mittendorf 2007, Hughes
and Williams 2008; Bagnoli and Watts 2010; Suijs and Wielhouwer 2014). Most existing literature treats ﬁrms’ private information as exogenous and does not consider the interaction between
ﬁrms’ information acquisition decisions and disclosure. Several theoretical studies simultaneously consider the problem of information acquisition and disclosure in an oligopoly market(e.g., Kirby 2004; Jansen 2008; Ganuza and Jansen 2013; Miwa 2019).3 In particular, Miwa
(2019) analyzes a Cournot duopoly model under demand uncertainty and shows that disclosure
negatively aﬀects ﬁrms’ incentives for acquiring information. This study tests and provides support for the theoretical predictions. The results demonstrate that although acquiring information
improves ﬁrms’ production decisions, disclosure diminishes ﬁrms’ incentives to do so. The results suggest that when information acquisition is endogenous and costly, mandatory disclosure
might have the unintended consequence of deteriorating ﬁrms’ internal information environment
and leading to ineﬃcient production decisions.
The second contribution is that this study complements prior archival-based research by
conducting a controlled experiment to test the theoretical predictions. In recent years, numerous
archival-based studies ﬁnd that product market competition aﬀects ﬁrms’ decisions about information disclosure (e.g., Bhojraj, Blacconiero, and D’Souza 2004; Guo, Lev, and Zhou 2004;
Dedman and Lennox 2009; Li 2010; Cheng, Man, and Yi 2013; Ali, Klasa, and Yeung 2014;
Dhaliwal, Huang, Khurana, and Pereira 2014). However, theoretical predictions derived fromthe existing disclosure models are very sensitive to some assumptions, such as types of information and competition (Suijs and Wielhouwer 2014). This makes it diﬃcult to test the theoreticalpredictions using archival-based data directly. For example, Dedman and Lennox (2009) ﬁnd
that ﬁrms are more likely to withhold information when the competition is intense in the industry, but they state that “we do not attempt to test predictions of a speciﬁc theoretical modelof disclosure” (p.214). This study uses an experimental economics approach and conducts acontrolled experiment, which allows the direct test of the theoretical model. As Ackert, Church,and Sankar (2000) point out, an experimental approach has several advantages in examining dis-3

Several studies examine information acquisition by ﬁrms in an oligopoly market, though they do not consider
the issue of disclosure (e.g., Li, McKelvey, and Page 1987; Hwang 1995; Hauk and Hurkens 2001).

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closure models.4 For example, researchers can create a controlled economic environment theywish to examine and directly observe ﬁrms’ behavior. In addition, researchers can compare theresults under diﬀerent conditions by manipulating the parameters of the environment.
Third, this study contributes to the growing literature on the relationship between ﬁrms’ internal and external reporting. Zimmerman’s (2014) textbook states that “the internal and externalreports are closely linked” (p.6) and points out that managers of large U.S. ﬁrms typically use
the same accounting procedures for both internal and external reporting. Hemmer and Labro(2008) argue that ﬁnancial reporting requirements and managerial decision making are closely
related, and they develop a model to examine the optimal relation between regulated ﬁnancial
reporting systems and unregulated management accounting information systems. Schneider and
Scholze (2015) analyze segment disclosure in an entry game and show that disclosure regulation that needs more transparency, such as management approach for segment reporting, might
negatively aﬀect ﬁrms’ information environment. Recent archival studies also suggest the link
between internal information systems and external reporting. For example, Dorantes, Li, Peters,
and Richardson (2013) ﬁnd that the implementation of enterprise systems, including enterprise
resource planning (ERP) and supply chain management system (SCM), improves ﬁrms’ internal information environment, and this leads to the improvement of the quality of management
forecasts. Shroﬀ (2017) ﬁnds that exogenous changes in accounting rules aﬀect ﬁrms’ investment decisions. This is an interesting result because accounting rules that are set for externalﬁnancial reporting also aﬀect ﬁrms’ internal decision making. Shroﬀ (2017) argues that thisis because some changes in accounting rules alter ﬁrms’ internal information environment andconsequently aﬀect their investment decisions. This study provides additional insights by examining the relationship between information acquisition decisions (internal reporting) and disclosure (external reporting) in the presence of product market competition. This study showsthat, in some situations, mandatory disclosure requirements negatively aﬀect ﬁrms’ incentives
for acquiring information, which in turn deteriorate ﬁrms’ internal information environment.
The remainder of this paper is organized as follows. Section 2 presents an overview of Miwa’s(2019) model that provides the basis for the experimental tests. Section 3 explains the experimental design. Section 4 reports the results, and Section 5 concludes this paper.

4

Several experimental studies investigate disclosure in duopoly markets (Cason 1994; Cason and Mason 1999;
Ackert et al. 2000). However, they do not consider ﬁrms information acquisition decisions preceding the disclosure.

52Theoretical background

I present an overview of Miwa’s (2019) model that provides the basis for the experimental tests.
Consider a single-period product market where two ﬁrms compete in quantities (i.e., a Cournot
duopoly market) under demand uncertainty. Assume that the market price p is determined by
the following inverse demand functionp = α − q1 − q 2 ,(1)

where q1 and q2 denote ﬁrm 1’s and ﬁrm 2’s quantity levels, respectively.5 The demand intercept
α isα = ᾱ + ∆α1 + ∆α2 ,(2)where ᾱ > 0 is a constant, and ∆αi is normally distributed with mean zero and variance s > 0,i.e., ∆αi ∼ N (0, s), i = 1, 2. It is assumed that ∆α1 and ∆α2 are independent.6 For simplicity,
the marginal cost of production is zero for both ﬁrms.
Each ﬁrm i acquires a signal ξi about ∆αi , which is costly and noisy. Speciﬁcally,
ξi = ∆αi + εi ,(3)where εi is a noise term and ε ∼ N (0, ei ). To acquire the signal, ﬁrm i must bear the informationacquisition cost Ki , which is assumed to be linear in 1/ei . Let k > 0 be a constant and deﬁne
ηi ≡ s/(s + ei ). Then, the information acquisition cost Ki can be written as
Ki (ηi ) =kηi.
s(1 − ηi )(4)

Following Miwa (2019), ηi ∈ [0, 1) is interpreted as the quality of the signal ξi . The higher ηiis, the more valuable the signal is. This is because ﬁrm i relies more on the signal to update
the prior belief when ηi is high, given that E[∆αi | ξi ] = ηi ξi . Whether the signal acquiredby ﬁrm i is disclosed or not is modeled as probability θi ∈ [0, 1]. That is, ﬁrm i’s signal ξi is
5

Miwa (2019) includes a parameter that represents the degree of substitution between ﬁrm 1’s and ﬁrm 2’s
products in the model. For simplicity, I assume that the two ﬁrms’ products are homogeneous in this study.
6
Miwa (2019) includes a parameter representing the degree of correlation between the two ﬁrms’ demand intercepts. Hence, his model can describe situations where the ﬁrms face industry-wide or ﬁrm-speciﬁc uncertainty
depending on the correlation. In this study, I focus on the case of industry-wide uncertainty.

6

publicly disclosed with probability θi and concealed with probability 1 − θi . I assume that theprobability θi is exogenous, and disclosure is truthful. When ﬁrm i’s signal ξi is disclosed, ﬁrm
j can observe and use the signal for its production decision. Both ﬁrms are assumed to be risk
neutral and maximize their own expected proﬁts.

2.1

Information acquisition decisions

Firm i’s ex ante expected proﬁt can be expressed as
h i

h i
 
E πi† = θi θj E πidd + (1 − θj ) E πidϕ

h i
h i
ϕd
+ (1 − θi ) θj E πi + (1 − θj ) E πiϕϕ .

(5)The superscript d (ϕ) denotes disclosure (nondisclosure). Firm i chooses the quality of thesignal to maximize the ex ante expected proﬁt net of the information acquisition cost. Therefore,
assuming that the optimal signal quality ηi∗ is obtained by an interior solution, the following ﬁrstorder condition holds.
∂  h †i
E πi − Ki (ηi )= 0.
∂ηi
ηi =ηi∗(6)

Consider the eﬀect of disclosure on ﬁrms’ information acquisition decisions. From the above
condition, one can obtain that ∂ηi∗ /∂θi < 0.7 This indicates that ﬁrms acquire less precise information when the acquired information is disclosed. In other words, disclosure negatively
impacts ﬁrms’ information acquisition decisions.8 In addition, regarding the eﬀect of the information acquisition cost, one can obtain that ∂ηi∗ /∂k < 0.

2.2

Production decisions

Why does disclosure negatively aﬀect ﬁrms’ information acquisition decisions? To clarify the
logic, consider the case where (i) both ﬁrms do not disclose their signals, and (ii) ﬁrm i discloses
its signal ξi , but ﬁrm j does not. When both ﬁrms do not disclose their signals, ﬁrm i’s and ﬁrm

7

See Miwa (2019) for the technical details.
Similarly, one can show that ∂ηi∗ /∂θj = 0, and hence ﬁrm i’s information acquisition decision is independentof ﬁrm j’s disclosure in this setting.
8

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j’s expected proﬁts can be calculated as
h
E

πiϕϕ

i

1
=
9




9
ᾱ + sηi ,4

h i 1
9
ϕϕ
2
E πj =ᾱ + sηj .
9
4

2

(7)

When only ﬁrm i discloses its signal ξi , ﬁrm i’s and ﬁrm j’s expected proﬁts are as follows.
h
E

πidϕ

i


1 2
=
ᾱ + sηi ,9
h i 1
9ϕd2
E πj =ᾱ + sηj + sηi .
9
4

(8)

h i
h i
The diﬀerence between E πiϕϕ and E πidϕ exhibits the proﬁt reduction for ﬁrm i caused byh i
h i
disclosing the signal ξi . In contrast, the diﬀerence between E πjϕϕ and E πjϕd exhibits the
additional proﬁt for ﬁrm j that it can earn by taking a free ride on ﬁrm i’s signal ξi .
The point is that the beneﬁt of acquiring information for each ﬁrm comes from adjusting its
production level through observing the signal. When both ﬁrms do not disclose their signals,
each ﬁrm observes only its own signal. In this case, ﬁrm i’s and ﬁrm j’s optimal quantity levels
are calculated as
1
qiϕϕ (ξi ) =
3




3
ᾱ + ηi ξi ,23ᾱ + ηj ξj .
3
2

1
qjϕϕ (ξj ) =(9)

On the other hand, when only ﬁrm i discloses its signal ξi , ﬁrm j can also observe ﬁrm i’s signal
ξi . Thus, ﬁrm i’s and ﬁrm j’s optimal quantity levels are as follows.
1
qidϕ (ξi ) = (ᾱ + ηi ξi ) ,33ᾱ + ηj ξj + ηi ξi .
3
2

1
qjϕd (ξj , ξi ) =(10)Note that ﬁrm i’s expected proﬁt for each case can be expressed as follows.
h i  h i2
h i
E πiϕϕ = E qiϕϕ
+ Var qiϕϕ ,h i  h i2
h i
E πidϕ = E qidϕ
+ Var qidϕ .

(11)
(12)

h i
h i
The expected quantity level for each case is equal and constant (i.e., E qiϕϕ = E qidϕ =(1/3)ᾱ). Thus, the key here is the variance of the quantity. From equations (9) and (10), ﬁrm
i adjusts its quantity level according to the signal value ξi . Such adjusting behavior increases
the variance of the quantity, which in turn increases the expected proﬁt. However, comparing
equations (9) and (10) indicates that the extent to which ﬁrm i adjusts its quantity level (i.e., theweight on ξi ) becomes smaller when ﬁrm i discloses its signal.
8

To explain the mechanism, consider the case where ﬁrm i obtains a signal ξi > 0. Observing
ξi > 0 means that the market demand is likely higher than the prior expectation, so ﬁrm iincreases its quantity level. As seen in equation (10), if the signal is disclosed, ﬁrm j also
observes it and increases its quantity level. That is, ﬁrm j can take a free ride on the signal
disclosed by ﬁrm i. Given that ﬁrms’ products are strategic substitutes in this model, an increasein production by ﬁrm j leads to a decrease in production by ﬁrm i. Thus, ﬁrm i increases its
quantity level, but the extent of the increase is not as large as under nondisclosure.
Conversely, when ﬁrm i obtains a signal ξi < 0, this means that the market demand islikely lower than the prior expectation. Thus, ﬁrm i decreases its quantity level. If the signal isdisclosed, ﬁrm j also decreases its quantity level. This leads to an increase in production by ﬁrm
i because of the eﬀect of strategic substitutes. Thus, in this case, ﬁrm i decreases its quantity
level, but the extent of the decrease is not as large as under nondisclosure.
In sum, acquiring information (i.e., a signal on the market demand) is beneﬁcial for ﬁrm i
because it allows ﬁrm i to adjust its production level depending on the market demand. However,disclosure of ﬁrm i’s signal reduces the extent to which ﬁrm i can adjust their production levels(i.e., the variance of ﬁrm i’s quantity), and this leads to a decrease in ﬁrm i’s expected proﬁt.
In other words, disclosure decreases the beneﬁt of acquiring information. Therefore, when theacquired information is disclosed, each ﬁrm acquires less precise information compared to thecase of nondisclosure.

3

Experimental design

I conduct an experiment on a Cournot duopoly market with stochastic demand. The experiment is based on a simpliﬁed version of Miwa’s (2019) model. To make the experiment simple
enough for participants to understand, I simplify some aspects of the model. In the experiment,
the information acquisition decision is a binary choice: whether or not to acquire information.
Speciﬁcally, if a ﬁrm chooses to acquire information, it bears the information acquisition costand receives a perfect signal about the actual demand state of the market. If a ﬁrm chooses notto acquire information, it does not receive any signals and remains uncertain about the market
demand. Furthermore, participants take the role of either a ﬁrm or a rival. Only the ﬁrm participants have a choice of whether or not to acquire information. The information acquisition cost,denoted by k, is a constant.

9I manipulate the information acquisition cost (low versus high) in two economic settings (disclosure versus nondisclosure). Hence, the experiment consists of four treatments: disclosure andlow cost (DL), nondisclosure and low cost (NL), disclosure and high cost (DH), and nondisclosure and high cost (NH). The experiment includes four sessions (one for each treatment), with
98 participants. Table 1 summarizes the experimental design.

Insert Table 1 about here.

I held all sessions at Osaka University in January 2012. I programmed and conducted theexperiment with the z-Tree software package (Fischbacher 2007). I recruited participants among
the undergraduate and master students from various departments. Upon arrival at the lab, participants drew lots and were assigned the role of either a ﬁrm or a rival, which did not change
throughout the session. Participants were then assigned a computer screen and received a set of
written instructions that the experimenter read aloud. The instructions used an economic frame(Huck 2004). The sessions consisted of 22 rounds. At the beginning of each round, ﬁrm/rival
pairs were randomly assigned. I used the random matching protocol to minimize potential repeated game eﬀects (e.g., reputation) because the experiment is based on a one-shot model.
Each round includes the following steps. First, a ﬁrm participant chooses whether or not
to acquire information about the market demand, about which there are three possible states:
Good, Medium, and Bad.9 The three demand states occur with equal probability. Next, the true
demand state appears on the ﬁrm participant’s computer screen if he or she decided to acquire
the information. Furthermore, in disclosure conditions (i.e., treatments DL and DH), the true
demand state also appears on the paired rival participant’s computer screen only if the ﬁrm
participant chose to acquire the information. In contrast, the rival participant cannot observe thedemand state in nondisclosure conditions (i.e., treatments NL or NH), regardless of the paired
ﬁrm participant’s choice.10 Finally, both the ﬁrm and the rival participants simultaneously selecttheir quantity levels and earn proﬁts.
The sessions lasted about 2 hours, including instruction time. After the instruction was read, I
conducted one trial round and then started the ﬁrst round. At the end of the session, participants
9

In the experimental instruction, I used the terms “state 1,” “state 2,” and “state 3” to refer to Good, Medium,and Bad, respectively.
10
Note that a ﬁrm participant can choose not to acquire information even in disclosure conditions. It can beinterpreted that the disclosed information has no information content in this case.

10were paid according to their total proﬁts earned throughout the 22 rounds. The average cash
payment was 3,825 yen (about 47.8 dollars) across all treatments.
As stated earlier, there are three demand states in the experiment: Good, Medium, and Bad.
Speciﬁcally, the inverse demand function for each state is as follows.
p = 240 − qf − qr

when the demand state is Good,(13)

p = 180 − qf − qr

when the demand state is Medium, and(14)

p = 120 − qf − qr

when the demand state is Bad,(15)

where qf and qr denote a ﬁrm’s and a rival’s quantity levels, respectively. In low-cost conditions(i.e., treatments DL and NL), the information acquisition cost is k = 100 while in high-costconditions (i.e., treatments DH and NH), it is k = 500. For simplicity, participants choose theirquantity levels in intervals of 5, i.e., {25, 30, 35, . . . , 85, 90, 95}, between 25 and 95. I used three
types of payoﬀ tables to calculate proﬁt, which corresponded to each demand state, which were
provided to participants.
Tables 2 and 3 summarize the theoretical predictions that provide the benchmarks for testing
the experimental results. The experiment is designed to test the following hypotheses, following
the model discussed in Section 2. My ﬁrst two hypotheses relate to ﬁrms’ information acquisition
decisions. In particular, I focus on the eﬀects of disclosure and the information acquisition cost.
The model suggests that disclosure negatively impacts ﬁrms’ information acquisition decisions.
Furthermore, as an intuitive consequence, I predict that increasing the information acquisition
cost also negatively aﬀects ﬁrms’ information acquisition decisions.
Hypothesis 1. Compared to when the acquired information is disclosed, the proportion of ﬁrms
acquiring information is greater when the acquired information is not disclosed.
Hypothesis 2. Compared to when the information acquisition cost is high, the proportion ofﬁrms acquiring information is greater when the information acquisition cost is low.

Insert Tables 2 and 3 about here.

Next, I focus on ﬁrms’ production decisions. The model suggests that acquiring information
is beneﬁcial for a ﬁrm because it allows the ﬁrm to adjust its production level depending on
11

the market demand. Note that this adjusting behavior increases the variance of the quantity,
which in turn increases the expected proﬁt. However, if the acquired information is disclosed, arival can also use the information and adjust its production level. In sum, disclosure triggers therival’s reaction that reduces the extent to which the ﬁrm can adjust its production level, leading
to a decrease in the ﬁrm’s expected proﬁt that disclosed the information. This explains why
disclosure decreases the beneﬁt of acquiring information. Therefore, my hypotheses on ﬁrms’
production decisions are as follows.
Hypothesis 3. If a ﬁrm acquires information, it adjusts its production level depending on the
demand state. While the ﬁrm increases the quantity when the state is Good, it decreases thequantity when the state is Bad.
Hypothesis 4. If a ﬁrm acquires information, and the information is disclosed, the paired rival
also adjusts its production level depending on the demand state. While the rival increases thequantity when the state is Good, it decreases the quantity when the state is Bad.
Hypothesis 5. Given that a ﬁrm acquires information, compared to when the acquired information is disclosed, the extent to which the ﬁrm adjusts its production level is greater when theacquired information is not disclosed.

4

Results

4.1 Information acquisition decisions
In this subsection, I examine ﬁrms’ information acquisition decisions. Table 4 presents the
proportion of ﬁrms acquiring information. Because each experimental session consisted of 22
rounds and there might exist some learning eﬀects, I present the data for the ﬁrst and last halves,in addition to the data for all rounds.

Insert Table 4 about here.

First, I investigate the impact of disclosure. I compare the proportion of information acquisition between disclosure and nondisclosure conditions. The proportion of ﬁrms acquiring
information in treatment NL is greater than that in DL. The diﬀerence is statistically signiﬁcant12

(p-value < 0.001 for both all rounds and last-half samples, Fisher’s exact test).11 In addition, thedata shows that the proportion in treatment NH is greater than that in DH, and the diﬀerence ismarginally signiﬁcant for all rounds sample (p-value = 0.097, Fisher’s exact test). For last-halfsample, the proportion in treatment NH is slightly greater than that in DH, but the diﬀerence is
not signiﬁcant (p-value = 0.385, Fisher’s exact test).
Next, I report the results for the eﬀect of information acquisition cost. I compare the proportion of information acquisition between low- and high-cost conditions. The proportion intreatment DL is greater than that in DH. Additionally, the proportion in treatment NL is greaterthan that in NL. The diﬀerences are statistically signiﬁcant (all p-values < 0.001, Fisher’s exacttest).
In sum, the results suggest that disclosure decreases a ﬁrm’s incentive to acquire information.
Furthermore, increasing the cost also negatively aﬀects a ﬁrm’s information acquisition decision.
These ﬁndings are consistent with the direction in the theoretical predictions and provide supportfor Hypotheses 1 and 2.
The regression results of probit models also conﬁrm these ﬁndings. Table 5 presents theestimated coeﬃcients from pooled probit and random eﬀects probit models. The dependent
variable is an indicator variable that equals one if a ﬁrm acquires information, and zero otherwise. The main independent variables are Disclosure and Cost. The variable Disclosure isan indicator variable that equals one in disclosure conditions (i.e., treatments DL and DH), andzero otherwise. Similarly, the variable Cost is an indicator variable that equals one in high-costconditions (i.e., treatments DH and NH), and zero otherwise. Speciﬁcations 2 and 4 include
the variable Round to capture some learning eﬀects. In all speciﬁcations, the estimated coefﬁcient on Disclosure is negative and statistically signiﬁcant. This implies that disclosure has
a negative impact on ﬁrms’ information acquisition decisions. The coeﬃcient on Cost is also
negative and statistically signiﬁcant. This indicates the negative eﬀect of increasing the information acquisition cost. Furthermore, the coeﬃcient on the interaction term between Cost andRound is negative and signiﬁcant under the random eﬀects probit model. This captures that in
high-cost conditions, the proportion of information acquisition tends to decrease over time, as
seen in Figure 1.

Insert Table 5 and Figure 1 about here.
11

The reported p-values are adjusted for multiple testing using Hochberg’s method.

13

4.2 Production decisions
4.2.1

The eﬀect of information acquisition

In this subsection, I investigate how information acquisition and disclosure aﬀect ﬁrms’ production decisions. First, I examine the eﬀect of information acquisition. The model and Hypothesis
3 predict that if a ﬁrm acquires information, it can adjust its production level depending on the
demand state. Hereafter, ﬁrms that acquire information are referred to as informed ﬁrms. Similarly, ﬁrms that do not acquire information are referred to as uninformed ﬁrms.
Table 6 and Panel A of Figure 2 present informed ﬁrms’ production decisions. The data
indicates that informed ﬁrms increase their quantity levels when the demand state is Good, while
they decrease when the demand state is Bad. Furthermore, the informed ﬁrms’ quantity levels
are well predicted by the theoretical model (see Table 2 and Panel A of Figure 1).

Insert Table 6 and Figure 2 about here.

I conduct Kruskal-Wallis test and Steel-Dwass multiple comparison test of informed ﬁrms’
production decisions. In all treatments, the Kruskal-Wallis and multiple comparison results
indicate that the diﬀerences among the quantity levels in each demand state (Good, Medium,or Bad) are statistically signiﬁcant (p-values < 0.001 for every combination of two demandstates). These suggest that informed ﬁrms choose diﬀerent quantity levels depending on themarket demand and provide support for Hypothesis 3.
Table 7 and Panel B of Figure 2 present uninformed ﬁrms’ production decisions. I conduct
Kruskal-Wallis test for uninformed ﬁrms’ production decisions. As expected, the null hypotheses
that there are no diﬀerences among the quantity levels in each demand state are not rejected in
all treatments (p-value = 0.558 in DL, p-value = 0.556 in NL, p-value = 0.636 in DH, andp-value = 0.347 in NH). That is, uninformed ﬁrms cannot adjust their output levels to match themarket demand. In sum, these results demonstrate that acquiring information improves ﬁrms’
production decisions.

Insert Table 7 about here.

144.2.2The eﬀect of disclosure

Next, I investigate the eﬀect of disclosure. Given that a ﬁrm acquires information, the paired
rival can receive the same signal and become informed in disclosure conditions, but it cannot
in nondisclosure conditions. The model and Hypothesis 4 predict that a rival also adjusts its
production level depending on the demand state if the paired ﬁrm acquired information in disclosure conditions. Table 8 and Panel A of Figure 3 present rivals’ production decisions when
the paired ﬁrms acquired information (i.e., informed rivals’ production decisions). The data indicates that informed rivals increase their quantity levels when the demand state is Good, while
they decrease when the demand state is Bad, in the same way as informed ﬁrms. I conduct
Kruskal-Wallis test and Steel-Dwass multiple comparison test for informed rivals’ production
decisions. In treatments DL and DH, the Kruskal-Wallis and multiple comparison results indicate that the diﬀerence in quantity levels in each demand state (Good, Medium, or Bad) is
statistically signiﬁcant (p-value < 0.001 for every combination of two demand states). On theother hand, in nondisclosure conditions, rivals cannot become informed even if the paired ﬁrms
acquired information. Hence, they cannot adjust production levels depending on the market
demand (see Table 8 and Panel B of Figure 3).
Insert Table 8 and Figure 3 about here.
This ﬁnding is conﬁrmed by the results of panel regression presented in Table 9. The dependent variable is rivals’ quantity levels. The variable Acquisition is an indicator variable that
equals one if the paired ﬁrm acquires information, and zero otherwise. The variable Good (Bad)is an indicator variable that equals one if the actual demand state is Good (Bad), and zero otherwise. The coeﬃcient on the interaction term between Acquisition and Good is positive andstatistically signiﬁcant in disclosure conditions. In addition, the coeﬃcient on the interaction
term between Acquisition and Bad is negative and statistically signiﬁcant in disclosure conditions. On the other hand, in nondisclosure conditions, the coeﬃcients on these interaction terms
are not statistically signiﬁcant. The results provide support for Hypothesis 4.
Insert Table 9 about here.
Because of the eﬀect of strategic substitutes, the extent to which an informed ﬁrm can adjust
its production level is predicted to be smaller if the paired rival uses the disclosed signal and15

adjusts its production level in the same direction. Table 6 and Figure 2 show that informed ﬁrms
increase their quantity levels when the demand state is Good and decrease when the demandstate is Bad. However, the data also suggest that informed ﬁrms in nondisclosure conditions (i.e.,treatments NL and NH) increase or decrease their quantity levels more than those in disclosure
conditions (i.e., treatments DL and DH).
First, I compare treatments DL and NL. When the demand state is Good, informed ﬁrms
produce an average of 82.9 units in treatment DL, which is less than the 90.3 units produced intreatment NL. The diﬀerence is statistically signiﬁcant (p-value < 0.001, Mann-Whitney test).
On the other hand, when the demand state is Bad, informed ﬁrms in treatment DL produces
an average of 39.7 units, which is more than the 33.6 units in treatment NL. The diﬀerence isalso signiﬁcant (p-value < 0.001, Mann-Whitney test). Next, I compare treatments DH and
NH. The diﬀerence in quantity level between the two treatments is signiﬁcant when the state is
Bad, but not signiﬁcant when the state is Good (Good: p-value = 0.013, Bad: p-value < 0.001,
Mann-Whitney test).
The results of panel regression presented in Table 10 conﬁrm the above ﬁnding. The dependent variable is ﬁrms’ quantity levels. In both disclosure and nondisclosure conditions, thecoeﬃcient on the interactive term between Acquisition and Good is positive and statistically signiﬁcant. However, the coeﬃcient on the interactive term in disclosure conditions is smaller thanthat in nondisclosure conditions. Similarly, in both disclosure and nondisclosure conditions, thecoeﬃcient on the interactive term between Acquisition and Bad is negative and statistically signiﬁcant. However, the absolute value of the coeﬃcient in disclosure conditions is smaller thanthat in nondisclosure conditions.

Insert Table 10 about here.

These results suggest that when the demand state is Good, informed ﬁrms in disclosure conditions tend to produce less than those in nondisclosure conditions. In contrast, informed ﬁrms
in disclosure conditions tend to produce more than those in nondisclosure conditions when the
demand state is bad. Given that a ﬁrm acquired information, the paired rival can also learn thetrue demand state and adjust its production level. That is, disclosing the demand information induces the rival to respond in the same direction, thus making the ﬁrm’s response to the acquired
information relatively small compared to the nondisclosure case because of the eﬀect of strategic
16

substitutes. Thus, rivals’ improved production decisions create a competitive disadvantage forthe paired ﬁrms because both compete in the same market. Therefore, the beneﬁt of acquiring
information decreases if the acquired information is disclosed. The results provide support for
Hypothesis 5.

4.3 Discussion
In this subsection, I discuss the experimental results that seem inconsistent with the theoreticalpredictions. First, the study does not ﬁnd experimental evidence consistent with the theory
concerning social welfare (see Table 11). This may be because both ﬁrms and rivals tend tohave higher outputs than the theoretical predictions when both are uncertain about the demandstate (see Table 12). One possible reason is that the production cost is assumed to be zero in theexperiment. I assume that the production cost is zero to avoid some eﬀects of loss aversion andsimplify the experiment. However, this assumption may lead participants to perceive that losses
from overproduction are relatively small.

Insert Tables 11 and 12 about here.

Next, I consider ﬁrms’ information acquisition decisions. Although the results on ﬁrms’ information acquisition decisions are consistent with the direction in the theoretical predictions
and provide support for the hypotheses, the result for each treatment deviates from the point
predictions derived from the theory. First, in treatment DH, the point prediction is that no ﬁrms
acquire information. However, the experimental result indicates that nearly half of the ﬁrms acquire information. This deviation from the point prediction might be explained by risk aversion.
By acquiring information, a ﬁrm can observe the actual demand state and thus resolve uncertainty about the demand. Furthermore, the untabulated result shows that compared to whenﬁrms do not acquire information, the variance of rivals’ quantity is signiﬁcantly lower whenﬁrms acquire information in disclosure treatments. This suggests that acquiring and disclosing
the information is useful for a ﬁrm to anticipate the rival’s strategy.
In treatments DL and NH, the point prediction is that all ﬁrms acquire information. In contrast, the result shows that only slightly more than half of the ﬁrms acquire information. A
certainty eﬀect might explain this deviation from the point prediction. The certainty eﬀect is17

a phenomenon that “people overweight outcomes that are considered certain, relative to outcomes which are merely probable” (Kahneman and Tversky 1979, p.265). In my experiment,
it is uncertain whether ﬁrms can enjoy the intended beneﬁt of information acquisition. This isbecause, even if ﬁrms resolve uncertainty about the demand by acquiring information, they still
face uncertainty about rivals’ behavior. The issue of uncertainty about rivals’ behavior might
become pronounced for ﬁrms, especially in nondisclosure conditions, because ﬁrms cannot provide information that inﬂuences the rivals’ behavior. Even though disclosure would be useful inanticipating the rivals’ behavior, some degree of uncertainty still remains. On the other hand, it
is certain that ﬁrms must bear the information acquisition cost if they acquire information. The
certainty eﬀect suggests that ﬁrms consider the information acquisition cost that must be bornewith certainty to be more important than the uncertain beneﬁts of acquiring information.

5

Conclusion

The experimental results are largely consistent with the theoretical predictions about informationacquisition choices and production decisions. The results demonstrate that disclosure decreases
a ﬁrm’s incentive to acquire industry-wide demand information when information acquisition iscostly and endogenous. Furthermore, I also show that ﬁrms improve their production decisions
by acquiring information. Thus, although acquiring information improves ﬁrms’ production
decisions, disclosure decreases a ﬁrm’s incentive to do so and thus harms the ﬁrm’s information
environment. This leads to ineﬃcient production, which in turn might have a substantial impact
on market outcomes.
This study has several limitations. For example, as discussed in the previous section, theassumption that the production cost is zero may unintentionally aﬀect participants’ behavior.
Furthermore, I point out that participants’ information acquisition decisions can be explainedin terms of risk aversion or a certainty eﬀect. Therefore, future research can modify the design
and replicate the experiments to test these possibilities. In addition, this study uses a random
matching protocol to test the static model; however, repeated interactions among the same players may provide a more appropriate reﬂection of reality. Repeated interactions can create theopportunity for tacit collusion, and thus the results might be diﬀerent from the static setting.

18

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22

Figure 1: Proportion of information acquisition, by treatment
1.0

Proportion

0.8

Treatment
DH
DL
NH
NL

0.6

0.4

0

5

10

15

Round

23

20

Figure 2: Informed ﬁrms’ quantity levels
Panel A: Disclosure conditions

Quantity (mean)

80

Treatment
60

DH
DL

40

0

5

10

15

20

Round

Panel B: Nondisclosure conditions

Quantity (mean)

80

Treatment
60

NH
NL

40

0

5

10

15

20

Round

Note: The dashed line shows the predicted quantity level when the demand state is Good foreach condition. The dot-dashed line shows the predicted quantity level when the demand state is
Medium for each condition. The dotted line shows the predicted quantity level when the demandstate is Bad for each condition. Across all treatments, the actual demand state is Good in rounds
4, 6, 10, 12, 14, 19, and 22; Medium in rounds 1, 3, 5, 8, 13, 16, 18, and 20; Bad in rounds 2, 7,
9, 11, 15, 17, and 21.

24

Figure 3: Rivals’ quantity levels when the paired ﬁrms acquired information
Panel A: Disclosure conditions

Quantity (mean)

80

Treatment
60

DH
DL

40

0

5

10

15

20

Round

Panel B: Nondisclosure conditions

Quantity (mean)

80

Treatment
60

NH
NL

40

0

5

10

15

20

Round

Note: The dashed line shows the predicted quantity level when the demand state is Good foreach condition. The dot-dashed line shows the predicted quantity level when the demand state is
Medium for each condition. The dotted line shows the predicted quantity level when the demandstate is Bad for each condition. Note that in nondisclosure conditions, rivals are always uncertain
about the demand state regardless ﬁrms’ information acquisition decisions. Across all treatments,
the actual demand state is Good in rounds 4, 6, 10, 12, 14, 19, and 22; Medium in rounds 1, 3, 5,
8, 13, 16, 18, and 20; Bad in rounds 2, 7, 9, 11, 15, 17, and 21.

25

Table 1: Experimental design
Information acquisition cost
Low (k = 100)

High (k = 500)

DisclosureDL
26 participantsDH
22 participants

NondisclosureNL
24 participantsNH
26 participants

Table 2: Theoretical predictions: Information acquisition and quantity level
Quantity
Treatment

DL

NL

DH

NH

Informationacquisition

Demand

Firm

Rival

Yes

Good
Medium
Bad

80
60
40

80
60
40

Yes

Good
Medium
Bad

90
60
30

60
60
60

No

Good
Medium
Bad

60
60
60

60
60
60

Yes

Good
Medium
Bad

90
60
30

60
60
60

26

Table 3: Theoretical predictions: Proﬁt and consumer surplus
ProﬁtTreatment

Demand

Firm

Rival

Consumer
surplus

DL

Good
MediumBad
Expectation

6300
3500
1500
3767

6400
3600
1600
3867

12800
7200
3200
7733

NL

Good
MediumBad
Expectation

8000
3500
800
4100

5400
3600
1800
3600

11250
7200
4050
7500

DH

Good
MediumBad
Expectation

7200
3600
0
3600

7200
3600
0
3600

7200
7200
7200
7200

NH

Good
MediumBad
Expectation

7600
3100
400
3700

5400
3600
1800
3600

11250
7200
4050
7500

Note: In treatments DL, NL, and NH, both ﬁrms’ proﬁts and consumer surplus are calculated,
given that a ﬁrm acquires information, and a ﬁrm’s proﬁt is the proﬁt after subtracting the information acquisition cost. In treatment DH, both ﬁrms’ proﬁts and consumer surplus are calculated,
given that a ﬁrm does not acquire information.

27

Table 4: Information acquisition by ﬁrms
Panel A: Proportion of information acquisition
All rounds

First half

Last half

DL treatment

64.3%

64.3%

64.3%

NL treatment

89.4%

91.7%

87.1%

DH treatment

47.1%

53.7%

40.5%

NH treatment

54.5%

62.9%

46.2%

Panel B: Fisher’s exact test with p-values adjusted by Hochberg’s method
All rounds

First half

Last half

p-valuep-valuep-value

DL vs. NL< 0.001< 0.001< 0.001

DH vs. NH

0.097

0.269

0.385

DL vs. DH< 0.001

0.269< 0.001

NL vs. NH< 0.001< 0.001< 0.00128

Table 5: Probit models: Information acquisition by ﬁrms
ProbitDisclosure

Cost
Disclosure × Cost

(1)

(2)

(3)

(4)

-0.880∗∗-1.073∗∗-1.681∗∗-1.942∗∗∗(0.378)(0.422)(0.662)(0.719)-1.134∗∗∗-0.862∗∗-1.912∗∗∗-1.410∗∗(0.385)(0.413)(0.659)(0.714)

0.694

0.695

1.184

1.217

(0.544)(0.550)(0.924)(0.961)Round-0.016-0.021(0.019)(0.018)

0.016

0.018

(0.019)(0.018)-0.024-0.049∗∗∗(0.019)(0.018)Disclosure × Round
Cost × Round

Constant

Log (pseudo)likelihood
Observations

Random eﬀects probit

1.248∗∗∗

1.436∗∗∗

2.285∗∗∗

2.578∗∗∗(0.293)(0.340)(0.501)(0.559)-639.996-632.256-420.007-405.434

1078

1078

1078

1078

Note:

The dependent variable is an indicator variable that equals one if a ﬁrm acquires information, and zero otherwise. Reported results are estimated coeﬃcients. Standard errors inparentheses. In speciﬁcations (1) and (2), standard errors are clustered at the participant level.
* p < 0.1, ** p < 0.05, *** p < 0.01

29

Table 6: Informed ﬁrms’ quantity levels
DemandTreatment

Good

Medium

Bad

DL

Mean
(SD)
MedianObservations

82.9(8.06)
80
58

62.0(8.03)
60
67

39.7(4.14)
40
59

NL

Mean
(SD)
MedianObservations

90.3(5.99)
9574

60.1(7.60)
6085

33.6(8.22)
30
77

DH

Mean
(SD)
MedianObservations

81.9(8.88)
80
34

61.5(9.94)
60
39

39.9(4.54)
40
41

NH

Mean
(SD)
MedianObservations

86.7(7.32)
85
48

60.7(8.78)
60
59

30.3(6.80)
30
49

30

Table 7: Uninformed ﬁrms’ quantity levels
DemandTreatment

Good

Medium

Bad

DL

Mean
(SD)
MedianObservations

78.0(13.0)
7533

77.0(12.9)
7537

73.4(17.3)
75
32

NL

Mean
(SD)
MedianObservations

84.5(6.85)
85
10

79.5(8.79)
8511

80.7(14.3)
85
7

DH

Mean
(SD)
MedianObservations

72.9(14.8)
7043

72.8(15.1)
7049

69.7(17.0)
67.5
36

NH

Mean
(SD)
MedianObservations

73.0(10.1)
7043

70.4(12.7)
7045

70.0(11.1)
70
42

31

Table 8: Rivals’ quantity levels when the the paired ﬁrms acquired information
DemandTreatment

Good

Medium

Bad

DL

Mean
(SD)
MedianObservations

79.2(10.9)
80
58

63.4(8.85)
60
67

41.5(7.21)
40
59

NL

Mean
(SD)
MedianObservations

66.2(12.3)
62.5
74

68(12.0)
6585

65.5(11.6)
60
77

DH

Mean
(SD)
MedianObservations

80.9(10.5)
80
34

59.9(7.99)
60
39

41.1(7.87)
40
41

NH

Mean
(SD)
MedianObservations

67.8(9.33)
70
48

66.1(13.8)
70
59

62.0(11.2)
60
49

32

Table 9: The eﬀect of information acquisition on rivals’ production decisions
(1)

(2)

Disclosure conditions

Nondisclosure conditions

Acquisition

0.686

0.514

(2.464)(1.768)

1.015

3.967

(1.669)(2.954)1.001-0.717(1.802)(2.385)16.067∗∗∗-3.394(1.868)(3.444)-22.350∗∗∗-2.114(2.015)(2.744)61.835∗∗∗65.755∗∗∗(1.376)(1.434)

Individual FE

Yes

Yes

adj. R2

0.506

0.023

Observations

528

550

Good

Bad
Acquisition × Good
Acquisition × Bad

Constant

Note: The dependent variable is rivals’ quantity levels. Standard errors (clustered at the participant level) in parentheses.
* p < 0.1, ** p < 0.05, *** p < 0.01

33

Table 10: The eﬀect of information acquisition on ﬁrms’ production decisions
(1)

(2)

Disclosure conditions

Nondisclosure conditions-12.975∗∗∗-11.779∗∗∗(3.354)(2.823)0.686

2.697∗∗(1.446)(1.244)-3.546-0.178(2.662)(1.608)19.906∗∗∗25.965∗∗∗(1.928)(1.782)-18.240∗∗∗-28.032∗∗∗(2.825)(2.211)74.715∗∗∗72.156∗∗∗(1.982)(1.870)Individual FE

Yes

Yes

adj. R2

0.677

0.862

Observations

528

550

Acquisition

Good

Bad
Acquisition × Good
Acquisition × Bad

Constant

Note: The dependent variable is ﬁrms’ quantity levels. Standard errors (clustered at the participant level) in parentheses.
* p < 0.1, ** p < 0.05, *** p < 0.01

34

Table 11: Proﬁt and consumer surplus
ProﬁtTreatment

Firm

Rival

Consumer
surplus

DL

Mean
(SD)

3604.6(2066.7)

3630.8(1875.38)

8136.6(4286.8)

NL

Mean
(SD)

3575.4(2886.6)

3323.9(1747.0)8480.0(3412.7)

DH

Mean
(SD)

3726.8(3076.5)

3215.0(2629.6)

8607.6(2469.5)

NH

Mean
(SD)

3211.5(2729.1)

3523.6(1750.8)8140.1(3478.6)

Note: In treatments DL, NL, and NH, samples are restricted to informed ﬁrms and the paired
rivals. In treatment DH, samples are restricted to uninformed ﬁrms and the paired rivals. For
low-cost conditions, the model predicts that a ﬁrm’s proﬁt: DL < NL, the rival’s proﬁt: DL >NL, consumer surplus: DL > NL. For high-cost conditions, the model predicts that the ﬁrm’s
proﬁt: DH < NH, the rival’s proﬁt: DH = NH, consumer surplus: DH < NH.

35

Table 12: Quantity levels of uninformed ﬁrms and the paired rivals
Quantity
Treatment
DL

NL

DH

NH

Firm

Rival

Mean
(SD)
MedianObservations

76.2(14.4)
75
102

62.2(17.6)
60
102

Mean
(SD)
MedianObservations

81.6(9.55)
8528

64.8(15.8)
65
28

Mean
(SD)
MedianObservations

72.0(15.5)
70128

62.7(14.4)
65
128

Mean
(SD)
MedianObservations

71.2(11.3)
70130

65.5(13.9)
65130

36