GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 326

Endogenous Information Acquisition andPartial Announcement Policy

Hiroki Arato, Takeo Hori and Tomoya Nakamura

January 2014; revised April 2014

GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

Endogenous Information Acquisition and the Partial
Announcement Policy∗
Hiroki Arato†

Takeo Hori‡

Tomoya Nakamura§

Shinshu University

Aoyamagakuin University

Osaka University

January 8, 2014, Revised March 19, 2014
Abstract
We consider implementability and the welfare eﬀects of a partial announcement
policy using a model of a beauty contest where agents’ actions are strategic complements and where their decisions on public information acquisition are endogenous.
The following results are obtained: i) if the authorities sell public information at aconstant price, multiple equilibria emerge and a partial announcement equilibriumis unstable; ii) here exist pricing rules that ensure the uniqueness and stability of
mixed strategy equilibria, which indicates that a partial announcement policy canbe implemented; iii) the optimal price of public information rises as its precision
increases relative to private information; iv) the optimal price is independent of thedegree of strategic complementarity.
Keywords: Beauty contest games; Endogenous information acquisition; Transparency of information; Partial announcement policy
JEL classification: C73, D82, D83, and E5∗

The authors are grateful to Akifumi Ishihara, Munechika Katayama, Keiichi Morimoto, Takashi
Shimizu, Yosuke Yasuda, the participants of the Contract Theory Workshop, the Economics Seminar at
Tokyo Metropolitan University, the Applied Microeconomics Workshop and the Applied Macro Seminarat Kyoto University, and the Japanese Economic Association meeting at Toyama University.
†
E-mail address: arato@shinshu-u.ac.jp‡
E-mail address: t-hori@aoyamagakuin.jp§
E-mail address: nakamura@iser.osaka-u.ac.jp1

1

Introduction

The authorities provide much information regarding economic fundamentals to the
public. This information inﬂuences the behavior of market participants. Theoretical literature addresses whether publicly provided information improves social
welfare. In their seminal paper, Morris and Shin (2002) show that public information may induce excessive coordination of agents’ actions, leading to a detrimental
welfare eﬀect if those actions are strategic complements. They conclude that an
opaque policy can improve social welfare if the precision of public information is sufﬁciently low. Many researchers challenge their results.1 In their inﬂuential paper,
Cornand and Heinemann (2008) show that a partial-announcement policy, underwhich the authorities disseminate public information to a certain fraction of agents,
can alleviate the problem of excess coordination using the beauty contest model of
Morris and Shin (2002). Cornand and Heinemann (2008) conclude that, under an
optimal partial announcement, a transparent policy can ameliorate social welfare
regardless of the precision of public information.
For policy makers, an important issue is how to pursue a partial announcement
policy. If policy makers can know the optimal fraction of public information users
and also count the number of users, they could achieve partial announcement bydisclosing their information up to the optimal number of users in order of arrival.
However, it is not realistic to correctly count up to the level of millions or tensof millions of market participants. Naturally, Cornand and Heinemann (2008) describe plausible methods to exclude some fraction of the agents from acquiring the
1

James and Lawler (2011, 2012b) strengthen the result of an opaque policy. On the other hand, many
researchers show welfare-improving eﬀect of transparent policy, for instance, Hellwig (2002), Angeletosand Pavan (2004), Svensson (2006), Cornand and Heinemann (2008), Dewan and Myatt (2008, 2012),
Arato and Nakamura (2011, 2013), and Myatt and Wallace (2014). Moreover, Angeletos and Pavan (2007)
and Ui and Yoshizawa (2013) show necessary and suﬃcient conditions that social welfare is improved bytransparent policies in quadratic Bayesian games under incomplete information with normal noises.

2

information.2 However, because the fraction of information users is exogenously
given in their model, they omit a model-based analysis. In the present paper, we
endogenize the fraction of information users and then attempt to design a simple and realistic policy instrument that can achieve the socially optimal partial
announcement policy.
To endogenize the fraction of information users, we assume that each agent has
to pay a usage fee to acquire public information. If the usage of public information
generates a larger payoﬀ than not using public information, an agent decides to pay
usage fee and become an information user. As a result, the fraction of information
users is endogenized. Using this simple framework, we examine the features ofusage fees that implement a partial announcement policy and then characterize thesocially optimal usage fee for public information.
Initially, we ﬁnd that it is not easy for the authorities to implement a partial
announcement by selling information at a certain price. When agents’ actions are
strategic complements, information acquisitions are also strategic complements, as
shown by Hellwig and Veldkamp (2009).3 If the authorities sell public information at a certain price, such strategic complementarity causes multiple equilibria,
which consists of two pure strategy equilibria (full- and no-announcement equilibria), and a mixed strategy equilibrium (a partial-announcement equilibrium).
The partial-announcement equilibrium is unstable. Hence, unless the authorities
could completely coordinate the beliefs of all agents, it would be diﬃcult to realize the partial-announcement equilibrium by selling information at a certain price.
2

See page 730 in Cornand and Heinemann (2008).
There are other studies regarding endogenous information acquisition in the literature of beauty
contest games. Colombo and Femminis (2008) study the model of Morris and Shin (2002) that is
extended by introduction of liner cost functions regarding acquisition of signal precisions. Myatt andWallace (2012) show that the cause of multiplicity as in Hellwig and Veldkamp (2009) is closely related toforms of cost functions regarding information acquisition. Colombo et al. (2013) and Ui (2013) analyze
welfare eﬀect of information acquisition under general strategic situations. In contrast to these studies,
we focus on stability of a partial announcement equilibrium from a view point of policy implementation.
33

As shown by Cornand and Heinemann (2008), if the fraction of information users
is exogenously given, a partial-announcement policy may alleviate over coordination caused by strategic complementarities. However, our analysis implies that, if
each agent faces a decision whether to acquire public information, strategic complementarities caused by the acquisition of public information may disturb the
implementation of a partial announcement.
To ensure the uniqueness and stability of the partial-announcement equilibrium,
we propose another pricing rule of information. If the authorities oﬀer a pricing
rule that counteracts the strategic complementarities of information acquisition,
they can coordinate the agents’ expectation, and hence, the partial announcement
is implementable. One such pricing rule is that the price of public information is
suﬃciently increasing in relation to the number of public information users. Thismethod involves a strategic substitution eﬀect and makes mixed strategy equilibrium stable.4
We next show that there exists the socially optimal usage fee that implements
the socially optimal level of publicity. The socially optimal usage fee is determinedby the relative precision of public information to private information and the degreeof coordination motive. It is shown that, if the relative quality of private information
decreases, the optimal degree of publicity and the optimal usage fee increases.
The reason is as follows. The relative worsening of private information accuracy
makes the over coordination problem less serious; therefore, the authorities should
increase the degree of publicity. Then, the authorities should increase the usage fee
to strengthen the agent’s incentive to acquire public information. Such an optimal
pricing strategy may seem strange because suppliers who want to increase quantity
4

Hellwig and Veldkamp (2009) and Myatt and Wallace (2012) also propose the ways to ensure equilibrium uniqueness. They propose the ways to realize a unique pure strategy equilibrium. In contrast, we
propose a way to make the mixed strategy equilibrium unique, because the mixed strategy equilibrium
corresponds to a partial-announcement one.

4

sell at a lower price under ordinary economic circumstances. This counterintuitive
result comes from the strategic complementarities on information acquisition. The
agent’s private beneﬁt of public information increases with the number of public
information users, and therefore, the market demand curve of public information
is upward sloping.
The optimal usage fee is independent of the degree of strategic complementarity.
A higher degree of strategic complementarity has two opposite eﬀects. On one hand,the optimal degree of publicity decreases because the excess coordination problem
becomes more serious. This eﬀect makes the optimal usage fee lower through the
upward-sloping demand curve of public information. On the other hand, the demand curve shifts upward because the private value of public information rises.
This eﬀect increases the optimal usage fee. In our model, these two eﬀects cancel
one another.
As mentioned above, although Cornand and Heinemann (2008) omit modelbased analyses, they describe plausible methods to implement a partial announcement policy. It should be noted that our modeling strategy of endogenizing thefraction of public information users is closely related to one of the methods discussed in Cornand and Heinemann (2008). More speciﬁcally, they state that by“selling data at prices that not all agents are willing to pay,” the authorities could
implement a partial announcement policy. The present study complements thediscussion of Cornand and Heinemann (2008) because we provide a model-based
analysis of “selling data at prices that not all agents are willing to pay” by extending
their model.55James and Lawler (2012a,b) also extend the model of Cornand and Heinemann (2008). Their concerns are diﬀerent from ours. James and Lawler (2012a) study eﬀects of a partial-announcement policy
under heterogeneous precision of private signals. James and Lawler (2012b) analyze a relationship between a partial announcement policy and a stabilization policy in their previous study (James and Lawler,2011).

5

Here we brieﬂy discuss why we focus on the method of “selling data at pricesthat not all agents are willing to pay.” We agree that all methods proposed by Cornand and Heinemann (2008) are eﬀective in implementing partial announcement
policies. However, other methods (except for the selling of information) raise thequestion of fairness because these methods may exogenously determine the fractionof information users. For instance, Cornand and Heinemann (2008) state that if
the authorities can “launch information in selected media,” then they can control
the degree of publicity. In this case, market participants who would like to know
the policy makers’ information may not be given a fair chance to acquire it. Moreover, if policy makers have rights to select media, speciﬁc media may be excluded
arbitrarily. In comparison with other methods, the method of selling information
has advantage of fairness because the authorities can give all the market participants a fair chance to acquire information under equal conditions. Whether toacquire information at the prices displayed then becomes an individual decision foreach market participant. Furthermore, under the assumption that the authorities
sell public information, we can easily endogenize the fraction of public information
users. Thus, the method of selling information is well suited to a model-based
analysis of a partial announcement policy.
This paper is organized as follows. Section 2 describes the model, and Section
3 shows the multiplicity of equilibria under certain prices. In Section 4, we present
a solution to survive a partial announcement equilibrium. We deal with welfare
implications in Section 5. Finally, in Section 6, conclusions are provided.

6

2

The Model

We borrow our basic model from Cornand and Heinemann (2008). However, departing from their model, we assume that each agent must pay a usage fee to acquire
public information.

Payoﬀ structure There are the authorities and a continuum of agents indexedby i ∈ [0, 1]. Each agent i chooses an action ai ∈ R to maximize the following
payoﬀ:ui (a, θ) = −(1 − r)(ai − θ)2 −r(Li − L̄) −Ti + τ ,
|
{z
}|
{z
} | {z }Loss 1

Loss 2(1)

Usage fee

where a ≡ {ai : i ∈ [0, 1]} is an action proﬁle, θ ∈ R is an unobservable state, andr ∈ (0, 1) is a parameter that represents the degree of strategic complementarity ofaction. Loss 1 is a standard loss. Agent i suﬀers a loss from a distance between ai∫1and θ. Loss 2 is a beauty contest loss. Li ≡ 0 (ai − aj )2 dj indicates that agent i
incurs a loss from distances between ai and others’ action aj . Loss 2 has zero-sum∫1structure because L̄ ≡ 0 Lj dj. Agents who use public information are called users
and others are called non-users. The share of users is denoted as P ∈ [0, 1]. In
contrast to Cornand and Heinemann (2008), P is an endogenous variable. The
authorities charge a constant usage fee for public information, T , and

Ti ≡




T,

if agent i uses public information,



0,

otherwise.

τ is lamp-sum transfer from the authorities to agents. Financial resource of τ istotal fee, τ = P T . From (1), agent i’s optimal action is ai = (1 − r)Ei (θ) + rEi (ā),∫1where ā = 0 ai di is an average action.

7

Information structure Information structure is as follows. Assume that allerror terms are independent mutually. The state θ is uniformly distributed on R.
After nature draws θ, agent i receives a private signal xi = θ+i with i ∼ N (0, 1/β).
The authorities also receive a public signal y = θ + η with η ∼ N (0, 1/α), anddisclose it only to users. In this setting, users’ and non-users’ estimations of θ are
i +αy
Eiu (θ) ≡ E(θ|xi , y) = βxβ+αand Ein (θ) ≡ E(θ|xi ) = xi , respectively.

Timing of the game The game has two stages. At stage 1, agents decide
whether to buy the public information, y, given T that is set by the authorities. At
stage 2, the authorities disclose y only to the users, and all agents receive xi andchoose ai .

3

Equilibrium

We solve the model by backward induction.
At stage 2, agents choose their actions, ai , given T and P . Because of additive
separability of our payoﬀ function, each agent’s equilibrium action strategy is thesame as in Cornand and Heinemann (2008).
Result 1. The equilibrium action of non-users is ain = xi , and the equilibriumβ(1−rP )action of users is aiu = κxi + (1 − κ)y, where κ ≡ α+β(1−rP).

At stage 1, each agent decides whether to use y, given P . Then, expected payoﬀ
of user is[
wiu (P ) ≡ E[uiu (a)|θ] = E − (1 − r)(aiu − θ)2
{∫ P
} ]
∫ 1
2
2
−r
(aiu − aju ) dj +(aiu − ajn ) dj − rL̄ θ − T + τ
0P(1 − rP )(1 − κ)2 r(1 − P ) + (1 + rP )κ2=−−+ rL̄ − T + τ,
α
β

8

(2)

Φ(P ), T

T
Φ(P )

O

Ppartial

1 P

Figure 1: Benefit from acquiring public information
and, similarly, the expected payoﬀ of non-user iswin (P ) ≡ −rP (1 − κ)2 [1 + r(1 − P )] + rP κ2−+ rL̄ + τ.
α
β

(3)

Agent i’s problem can be written as maxpi pi wiu (P )+(1−pi )win (P ), where pi ∈ [0, 1]
is a probability that agent i purchases public information. It is the agent i’s mixed
strategy. From (2) and (3), agent i’s net beneﬁt from receiving y is ∆wi (P ):∆wi (P ) ≡ wiu (P ) − win (P ) =α(α + β)− T ≡ Φ(P ) − T,β [α + (1 − rP )β]2

where Φ(P ) represents a gross beneﬁt of acquiring y. If the net beneﬁt is positive,
purchasing y is optimal for agent i. If negative, not buying y is optimal. If zero,
the two alternatives are indiﬀerent.
Figure 1 represents the cost and beneﬁt of acquiring y. Regardless of P , the cost
is constant because T is constant. On the other hand, the gross beneﬁt increases
with P ; Φ0 (P ) > 0. This is because the value of public information as a focal pointof others’ action increases when more agents use y. As a result, the net beneﬁt9∆wi (P ) = Φ(P ) − T is strictly increasing in P . Hence, for any T ∈ (Φ(0), Φ(1)),
there uniquely exists Ppartial ∈ (0, 1) such that Φ(Ppartial ) = T .6 Then, for all
agents, their best response function, R(P ), is




=0
if P < Ppartial ,R(P ) ∈ [0, 1] if P = Ppartial ,






= 1
if P > Ppartial .

(4)

As in Hellwig and Veldkamp (2009), R(·) indicates that public information acquisitions are strategic complements when actions are strategic complements. Public information is useful for inferring other users’ actions; hence, when actions are
strategic complements, the private value of public information becomes higher as
the number of information users increases.

Multiple equilibria and (in)stability A mixed strategy proﬁle, (pi ), is anequilibrium if, for all i, pi is a best response for the others’ strategy proﬁle p−i .
From the law of large numbers, P = R(P ) holds in a symmetric equilibrium.
We can easily verify that the strategic complementarities about informationacquisition cause multiple equilibria. Figure 2 represents the best response whenΦ(0) < T < Φ(1). pi = 0 (pi = 1) for all i is an equilibrium, because agent i’s best
response is pi = 0 (pi = 1) for p−i = 0 (p−i = 1). Moreover, pi = Ppartial ∈ (0, 1)
for all i, where Ppartial satisﬁes Φ(Ppartial ) = T , is also an equilibrium because
pi = Ppartial is a best response for p−i = Ppartial .
Lemma 1. Suppose that the authorities apply the constant pricing rule. Then,
1. If T ∈ (Φ(0), Φ(1)), then multiple equilibria arise as follows.
(a) No-announcement equilibrium: pi = 0 for all i, hence P = 0,
6

Partial announcement does not occur when T < Φ(0) or T > Φ(1).

10

R(P )
1

PpartialO

Ppartial

1

P

Figure 2: Best response dynamics and (in)stability of equilibrium(b) Full-announcement equilibrium: pi = 1 for all i, hence P = 1,(c) Partial-announcement equilibrium: pi = Ppartial for all i, hence P =Ppartial .
2. If T < Φ(0), full-announcement equilibrium exists uniquely. If T > Φ(1), noannouncement equilibrium exists uniquely. However, if T < Φ(0) or T > Φ(1),there does not exist any partial-announcement equilibrium.
Next, we deﬁne the stability of an equilibrium, following in the steps of Milgrom
and Roberts (1990) and Vives (1990). In what follows, we describe equilibrium byits outcome Pl (l = 1, 2, 3), where P1 = 0, P2 = Ppartial , and P3 = 1, correspond tono-announcement, partial announcement, and full-announcement, respectively. A
Cournot tatonnement in our game is deﬁned as the process {P (t)}: P (0) ∈ [0, 1],
P (t) ∈ R(P (t − 1)), t = 1, 2, · · · . We deﬁne the stability of equilibrium as follows.
Definition 1. When there uniquely exists an equilibrium, it is stable. When there
exist multiple equilibria, an equilibrium Pl ∈ [0, 1] is stable if there exists P (0) 6= Plsuch that the Cournot tatonnement starting at P (0) converges to Pl .

11

Figure 2 represents the best-response dynamics and equilibrium stability in
our information acquisition game. When P (0) ∈ [0, Ppartial ), the best-response
dynamics converges to P1 (= 0). When P (0) ∈ (Ppartial , 1], it converges to P3 (= 1).
Hence, the following proposition holds.
Proposition 1. Suppose that the authorities apply the constant pricing rule withT ∈ (Φ(0), Φ(1)). Then, no-announcement and full-announcement equilibria arestable, and a partial-announcement equilibrium is unstable.
Such equilibrium instability implies that coordination of the agents’ expectation
is essential to achieve partial dissemination of public information.

4

A Coordination Device of Expectation

We propose a solution that the authorities guide the agents to the unique partialannouncement equilibrium. The cause of the coordination failure is that, owing to
the strategic complementarities, ∆wi (P ) is upward sloping. To align the agents’beliefs, we employ another pricing rule that has a strategic substitution eﬀect.
Assume that the fee suﬃciently increases in the number of users. Formally, consider
a pricing rule T = Ψ(P ), where Ψ(P ) satisﬁes that< Φ(P ) if P < Ppartial ,Ψ(P ) = Φ(P ) if P = Ppartial ,






> Φ(P ) if P > Ppartial .

12Φ(P ), TR(P )1
T = Ψ(P )Φ(P )O

Ppartial

1 P

OPpartial

1 P

Figure 3: Increasing pricing rule and stability of equilibrium
We call it an increasing pricing rule.7 The strategic substitution eﬀect of Ψ(P )counteracts the strategic complementarities of information acquisition, and makes∆wi (P ) downward sloping. Then, the agents plausibly believe that P = Ppartial isrealized, because the agents’ best response function is




=1




R(P )

if P < Ppartial ,∈ [0, 1] if P = Ppartial ,






= 0
if P > Ppartial .

(5)Then, P = Ppartial is a unique equilibrium and hence stable (Figure 3).
Proposition 2. The authorities can implement partial-announcement policy tar7

In a theoretical viewpoint, Ψ(·) does not need to be continuous. For example, an extreme rule that
if P < Ppartial0Ψ(P ) = Φ(Ppartial) if P = Ppartial∞
if P > Ppartial

satisﬁes the condition for uniqueness of a partial-announcement equilibrium. However, such a rule may
levy a huge payoﬀ loss on all users because of slightly excess demand by accident. Therefore, as to avoid
the loss, Ψ(·) should be continuous.

13

geting P = Ppartial ∈ (0, 1) by introducing the increasing pricing rule T = Ψ(P )such that:< Φ(P )




Ψ(P )

5

if P < Ppartial ,= Φ(P )> Φ(P )if P = Ppartial ,if P > Ppartial .

Welfare Implications

To focus our analysis on feasibility of a partial-announcement policy, we have thus
far omitted welfare implications. Thereby, we know that the authorities can achieve
any degree of publicity by devising the methods of pricing. However, to maximizesocial welfare, the authorities should disclose their information only to an optimal fraction of agents by setting T at stage 0. This section studies the welfare
implications of a partial announcement and optimal pricing.

5.1

Social welfare and the optimal degree of publicity

We deﬁne social welfare as an (normalized) average of individual payoﬀ:
1
W (a|θ) ≡1−r∫ 1

ui di = −0(∫ P(aiu − θ) di +

∫ 1

2

0

)
(ain − θ) di .
2

(6)

P

Substituting equilibrium actions (result 1) into (6) yields the following equilibriumsocial welfare:E[W (a|θ)] = −P

α + (1 − rP )2 β
1
− (1 − P ) .
2[α + (1 − rP )β]β14

Then, if α/β < 3r − 1, the optimal fraction of user P ∗ is∂E(W )
3r(1 − r)α(α + β)=∂P[α + (1 − rP )β]3

(

α+β
−P
3rβ

)

= 0 ⇔ P∗ =α+β∈ (0, 1),3rβ

(7)and if α/β ≥ 3r − 1, P ∗ = 1. This indicates that, if the relative precision of public
information is suﬃciently low, it is socially desirable that a partial set of agents use
public information.8
A partial announcement has two eﬀects. First, it limits the number of users.
This eﬀect lowers total precision of information in this economy, and it decreasessocial welfare. Second, it restricts the number of agents who can coordinate throughthe public information. This eﬀect alleviates the overreaction problem, and it
increases social welfare. If public information is suﬃciently precise (α/β ≥ 3r − 1),then the second eﬀect is dominated by the ﬁrst eﬀect. Therefore, P ∗ = 1 maximizessocial welfare. On the other hand, if public information has a suﬃciently low
precision (α/β < 3r−1), we need to consider tradeoﬀ of the two eﬀects. Then, there
exists a socially optimal partial announcement ratio P ∗ = (α + β)/(3rβ) ∈ (0, 1).
{}
Result 2. The socially optimal degree of publicity is defined as P ∗ = min 1, α+β
3rβ .

5.2

Optimal usage fee

In this subsection, we determine the socially optimal pricing rules that achieve P ∗ .
First, we consider the case where α/β ≥ 3r − 1, and hence P ∗ = 1. Then, theαauthorities can maximize social welfare by setting any T ∗ < Φ(0) = β(α+β).9 Next,

8This result is identical with that of Cornand and Heinemann (2008).
T < Φ(0) is a suﬃcient condition because, from Φ0 (P ) > 0, if the cost T is smaller than Φ(0), thenit is always optimal for agents to use y. T ∗ < 0 can be understood as subsidies for promotion of using
public information.
915

we examine the case where α/β < 3r − 1, and hence P ∗ = (α + β)/(3rβ). Then,
9αby substituting P ∗ into Φ(P ), we have T ∗ = 4β(α+β).

Proposition 3. Given α, β, and r. If the authority defines the usage fee of public
information as

T

∗




=

9α
4β(α+β) ,if α/β < 3r − 1,< α ,β(α+β)

if α/β ≥ 3r − 1,(8)then P ∗ is equilibrium.
Combining Propositions 2 and 3 and Result 2, the authorities can achieve asocially optimal partial-announcement equilibrium using the increasing pricing ruleT = Ψ∗ (P ) such that Ψ∗ (P ∗ ) = T ∗ and Ψ∗ (P ∗ ) ≷ Φ(P ∗ ) if P ≶ P ∗ .

Comparative statics We examine properties of the optimal usage fee T ∗ withrespect to the precision of public information α and private information β, andwith respect to the degree of strategic complementarity r. The following corollary
is derived from Proposition 3.
Corollary 1. Assume α/β < 3r − 1. Then,
∂T ∗
> 0,
∂α

∂T ∗
< 0,
∂β

∂T ∗
= 0.
∂r

Assume that quality of the authorities’ research improves and that they canprovide public information with higher precision. The optimal publicity P ∗ =(α + β)/(3rβ) increases because the excess coordination problem becomes less serious. Then, the authorities should increase usage fees to strengthen the agent’s
incentive to acquire public information. At a ﬁrst glance, such an optimal pricing
strategy may seem strange because suppliers who want to increase quantity sell

16

at a lower price under ordinary economic circumstances. This counterintuitive result emerges from the strategic complementarities on information acquisition. The
agent’s private beneﬁt of public information rises as the number of public information users increases; therefore, the market demand curve of public information is
upward sloping.10
If the quality of the agents’ private information rises, the optimal fraction of
public information users decreases. Then the authorities who face an upwardsloping demand curve should lower the usage fees of public information.
Finally, the optimal usage fee is independent of the degree of strategic complementarity. The higher degree of strategic complementarity has two opposite eﬀects.
On one hand, the optimal degree of publicity decreases because the excess coordination problem becomes more serious. This eﬀect decreases the optimal usage
fee through the upward-sloping demand curve of public information. On the other
hand, the demand curve shifts upward because the private value of public information rises. This eﬀect makes the optimal usage fee higher. In our model, these two
eﬀects cancel one another.

6

Conclusion

We have analyzed implementability and the welfare eﬀect of a partial-announcement
policy by selling public information. A model-based analysis of a public announcement by selling data provides some fruitful policy implications. We obtain thefollowing results.
First, we discover a way to implement a partial announcement policy by sellingdata. A partial-announcement policy is a solution for alleviating the over coordination problem generated by strategic complementarities in action. However, such
10

See the left panel of Figure 3.

17strategic complementarities transform information acquisition into strategic complements; therefore, any pricing rule that keeps the usage fee constant leads tomultiple equilibria. Hence, the strategic complementarities themselves may disturb
the implementation of a partial announcement if the authorities sell public information at certain prices. Nevertheless, there is a simple solution to the problem.
We show that a partial announcement equilibrium can be unique under some increasing pricing rules that counteract the strategic complementarity of informationacquisition; hence, a partial announcement policy is implementable.
Second, we characterize the socially optimal usage fee of public information. If
the quality of private information worsens, the authorities should increase the usage
fee of public information. The optimal usage fee is independent of the degree ofstrategic complementarity. These somewhat counterintuitive results originate fromthe upward-sloping demand curve for public information caused by the strategic
complementarities.
There are still some open questions. In our model, the accuracy of private
information is exogenous. If private information acquisition is endogenous as in
Colombo and Femminis (2008), Colombo et al. (2013), and Ui (2013), then its
accuracy depends on the properties of its acquisition cost function, the accuracy of
public information, and the degree of strategic complementarities. In this case, theoptimal pricing rule on a public announcement might change. This subject is left
for future research.

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