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Journal of Accounting and Economics 12 (1990) 219-243.
North-Holland
FINANCIAL DISCLOSURE POLICY IN AN ENTRY GAME*
Masako N. DARROUGH Columbia University, New York, NY 10027,
USA
Neal M. STOUGHTON
Universiv of California at Irvine, Irvine, CA 92717, USA
Received July 1988, final version received June 1989
This paper analyzes incentives for voluntary disclosure of
proprietary information. Proprietary information, if disclosed,
provides strategic information to potential competitors, but can be
helpful to the financial market in valuing the firm more
accurately. Focusing on a stylized model of a static entry game, we
show that a fully revealing disclosure equilibrium exists when the
prior of the market is optimistic or the entry cost is relatively
low. When the prior is pessimistic or the entry cost is high,
however, both non- and partial-disclosure equilibria obtain. Our
analysis predicts that competition in the product market encourages
voluntary disclosure.
1. Introduction
This paper analyzes voluntary disclosure of proprietary
information. An established incumbent firm is endowed with private
information. If disclosed, the information will help the financial
market in evaluating the firms value more accurately; the
disclosure, however, could compromise the incumbents competitive
position. by providing strategic information to potential competi-
tors. We focus on a relatively stylized model of a static entry
game, where the cost of disclosing proprietary information takes
the form of an increased probability of entry. Our model
endogenizes the cost by making the probabil- ity of entry an
optimal choice on the part of the entrant. The incentives are
countervailing. An incumbent with favorable information wishes to
communi- cate the information to the financial market to raise its
valuation, but other- wise does not want to make this known to the
potential entrant. An incumbent
*A substantial portion of this research project was carried out
while both authors visited the Anderson Graduate School of
Management at UCLA. The second author acknowledges a faculty
fellowship provided by the University of California at Irvine. We
would like to thank Yuk-Shee Chars. Jerry Feltham, Ron Giammarino,
Don Kirk, Vojislav Maksimovic, Henry McMillan, Eric Rasmusen,
Michael &linger, Tom Russell, Robert Verrecchia (the referee),
and participants in the seminars at Columbia, University of British
Columbia, Indiana University, University of Rochester, University
of California at Berkeley, Rutgers, and Stanford for helpful
comments.
01654101/90/$3.500 1990. Elsevier Science Publishers B.V.
(North-Holland)
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220 M. N. Darrough and N. M. Stoughton, Entry andjinancial
disclapure
with unfavorable information, on the other hand, would rather
not disclose this to the financial market, yet may want to
communicate this to the potential entrant to discourage entry. The
financial market, of course, has rational expectations taking into
account the impact of their conjecture on the firms incentive to
disclose and the entrants reaction in the product market. A
possible scenario we identify is as follows: an incumbent
voluntarily discloses unfavorable information to discourage entry,
yet the financial market reacts positively.
Three players (the incumbent firm, the potential entrant, and
the financial market) are needed to analyze the conflicting
incentives to disclose. The initial literature on disclosure
[Grossman (1981) and Milgrom (1981)] focusses on a situation
without the potential entrant, where the incumbent is only
concerned with financial market valuation. In this case the impetus
for disclosure is provided by the incumbents with favorable
information. The only equilibrium is one of full disclosure.
Without the financial market, but with a potential entrant, it is
easy to see that the only equilibrium is again one of full
disclosure. In this case the impetus for disclosure comes from
incumbents with unfavorable information who maximize their
intrinsic value by deterring entry. When all three players are
considered simultaneously, the possibility arises of partial
disclosure and nondisclosure equilibria because of the con-
flicting objectives of incumbents with favorable and unfavorable
information.
Three equilibria are identified as follows:
l A disclosure equilibrium in which private information is
disclosed (and entry depends on the information),
l A nondisclosure equilibrium in which private information is
not disclosed (and entry does not take place),
l A partial disclosure equilibrium in which favorable
information is never disclosed, but unfavorable information is
sometimes disclosed (and entry is random).
The first equilibrium obtains regardless of the prior beliefs,
while the second and third occur only when the prior is pessimistic
or the entry cost is relatively high.
Issues related to disclosure policy have been examined in
various contexts [Dye (1985a,b, 1986), Hughes (1986)]. Three papers
that are closer to the present paper are Verrecchia (1983),
Bhattacharya and Ritter (1983), and Gertner et al. (1988).
Verrecchia considers whether a manager exercises discretion in
disclosing or withholding information in the presence of
traders
For models of this sort see Vives (1984) and Gal-Or (1985,
1986).
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MN. Darrough and N. M. Stoughton, Entry and@ncial disclosure
221
who have rational expectations about his motivation. The
managers decision is based on the effect of information on the
assets market price. Assuming an exogenously determined proprietary
cost, the threshold level of disclosure is shown to be positively
correlated to the proprietary cost. Thus, Verrecchia suggests that
the nature of competition is important in determining the level of
disclosure. He states:
Firms in less competitive industries may see no costs associated
with making public disclosures. The corollary suggests that the
greater the proprietary cost associated with the disclosure of
information, the less negatively traders react to the withholding
of information.
Verrecchia concludes, therefore, that product market competition
may provide disincentives for voluntary disclosure. Although this
conclusion has an intu- itive appeal, our model will suggest a
rather different implication concerning the disclosure policy of a
firm facing a threat of entry. In our model, when the prior is
optimistic or the entry cost is relatively low, the unique
equilibrium is that of full disclosure. In other words, full
disclosure takes place when the market condition is favorable
enough to support two firms. This occurs because the motive for
entry deterrence becomes dominant for an incumbent with favorable
information. We would expect that lower costs of entry are
associated with greater competitive pressures. Thus our model
predicts that competition encourages voluntary disclosure.
Bhattacharya and Ritter (BR) model a winner take all innovation
game. A tirm with superior information decides on the level of
disclosure taking into account the impact on the financial market
in raising the necessary capital as well as the impact of the
rivals success probability in a R&D race. Although entry is
endogenous in the BR model, exogenous costs are also imposed. By
contrast, our model is game-theoretic and costs are endogenous. The
Gertner et al. article is chiefly concerned with a theory of
capital structure. An important difference between our model and
theirs is that we assume truthful disclosure instead of
constraining the contract process by this requirement.
Although we label specific variables as private information, our
motivation is quite general. Almost any information voluntarily
revealed through formal or informal channels, such as financial
statements, press conferences, or discussions with reporters, can
have strategic implications. Even a discussion on the nature of
R&D, future plans, or a management earnings forecast often
reveals useful information to competitors. This might be the reason
why few American corporations provide management forecasts.
The paper is organized as follows. The next section deals with
the descrip- tion of the game. The game is then analyzed in section
3, and equilibria are derived in section 4. The fifth section
discusses the interpretation of these equilibria. The paper closes
with a discussion and conclusion.
J.A.E.-H
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222 M. N. Durrough und NM Stoughton, Entry andfinancial
disclasure
2. Description of the game
We now present a formal model to describe the game among the
incumbent monopolist (I), the financial market, and the potential
entrant (E). The model consists of two dates and one period. At
time zero, the incumbent raises $K from the financial market by
selling a portion of the fhm2 The terms of financing are influenced
by the disclosure (or lack thereof) of the incumbents private
information, as is the potential entrants decision. If entry takes
place, a duopoly game is played at the end of the first period.3
Entry incurs a cost of $K,. Since the entrant does not have any
private information, the method of financing is of no consequence.
Upon entry, the entrant becomes informed, even if no disclosure was
made by the incumbent.
Before we can analyze the strategies of the incumbent and the
potential entrant, it is necessary to specify in detail the payoffs
of the players in the game. First it is necessary to understand how
revelation of the private information affects the profits of the
duopolists in the post-entry game. It is convenient to classify the
incumbent information as favorable or unfavor- able from the
viewpoint of the potential entrant. We then explain the assumptions
that were made as to the partial ordering of profits associated
with different outcomes of the game. Finally, strategies of the
players are defined to conclude the description of the game.
2.1. Informational consequences of the post-entry game
Consider the post-entry subgame. Upon entry, the entrant learns
the private information (regardless of whether the private
information was actually dis- closed or withheld by the incumbent).
The entrant then makes the optimal output decision to share the
market with the incumbent. Favorable (good) news is defined as
follows:
Dejinition. If the effect of a change in a parameter value (or
collection of parameter values) is to increase the realized profits
of both the incumbent and entrant in the post-entry game, then this
is fauorable news.
The news is unambiguously favorable to the entrant. For the
incumbent who is contemplating whether to disclose at a pre-entry
stage, the disclosure will increase the probability of entry of the
potential entrant. Thus in such a situation, the incumbent is
reluctant to release the private information. This
The financing method is equity issuance: in particular, we
assume that the firm is not able to borrow funds (either privately
or publicly).
This differs somewhat from the conventional entry game in which
the incumbent is a monopolist in the first period and its product
market behavior in the first period afkcts the entrants behavior in
the second period.
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M.N. Darrough and N. M. Stoughton, Entry and financial
disclasure 223
illustrates that a conflict of interest concerning disclosure by
the incumbent arises when the news affects the profits of the two
firms in the same direction in the post-entry game. Such a conflict
does not arise when the profits of the incumbent and entrant move
in opposite directions. The incumbent is pleased to disclose such
news, since it not only increases financial market valuation, but
also discourages entry. Therefore, a nontrivial disclosure problem
exists only if information fits our definition of favorable
news.
For illustration, in the appendix, we formulate a post-entry
subgame based on Cournot-Nash behavior with linear demand and cost
functions. The incumbent and the entrant are assumed to sell
differentiated products in the same market. We show that an
increase in the value of the demand intercept raises the
equilibrium profits of both duopolists and therefore fits our
defini- tion of favorable news. It can also be seen that the slope
of the demand curve and the coefficient of differentiation affect
the profits of duopolists in the same direction: the flatter the
demand curve, the higher the profits; the more differentiated the
products, the higher the profits.
The impact of production cost, on the other hand, is different.
If costs are independent, a lower marginal cost of the incumbent
increases its own profit but decreases the entrants profit, ceteris
paribm4 There are no tradeoffs to worry about. The potential
entrant, not having entered in the market, might not know its
marginal cost. If there is a positive correlation between the costs
of the two firms, low cost of the incumbent is favorable news to
the entrant, since the profits of the two firms move in the same
direction.5
By looking at the sign of these comparative statics, we classify
the informa- tion into favorable and unfavorable news. This
classification is based on the impact of information on the
entrants profitability. For the potential entrant, entry is more
profitable under a favorable condition and is less profitable under
an unfavorable condition. The incumbent, on the other hand, has to
consider the tradeoffs between the impact on the entry behavior as
well as the financial market reaction. The financial market in turn
would value the incumbent by assessing the strategies of both the
incumbent and the entrant. It should be emphasized that the
qualitative analysis and predictions of our model do not depend on
the Coumot structure. They do assume, however, that the post-entry
game does not degenerate to a situation in which profits are driven
down so low that entry is never warranted.
2.2. Partial ordering of projits
Now that favorable and unfavorable news are defined, we relate
the duopoly profit levels to those of the disclosure/entry game.
The incumbent is con-
4This is the case analyzed by Milgrom and Roberts (1982) in the
context of limit pricing. Harrington (1986) analyzes this case to
show that the monopolist may charge a higher price
than the monopoly price.
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224 M. N. Darrough and N. M. Stough~on, Entry ond financial
discloswe
cemed with the two effects of disclosure, since entry reduces
its profit but it needs financing from the financial market. We
assume that the private infor- mation parameters take on two
possible values, H or L (high or low). For ease of exposition, we
refer to the incumbent with favorable information as type H and the
one with unfavorable information as type L. These values are common
knowledge. Thus the following notation is used to represent the
(actual or intrinsic) profit levels of the incumbent (I) and the
potential entrant (E) when the private information is favorable or
unfavorable.
i9 i = M, I, E, the profit of monopolist (M), incumbent (I), and
entrant (E) under duopoly when the condition is favorable,
ni? i = M, I, E, the profit of monopolist (M), incumbent (I),
and entrant (E) under duopoly when the condition is
unfavorable.
These definitions imply that
i7; > ai? i=M,Z, E.
For the potential entrant to have a nontrivial entry problem, we
assume that:
[Al] ?i,>&>&o.
This guarantees that if a disclosure of unfavorable information
is made, the potential entrant will stay out but will surely enter
if a disclosure of favorable information is made.
What is nor implied by our definition is the relation between
II, and fi,. It turns out that these two values are critical in the
disclosure/entry game. Therefore we need to understand what this
relation implies. Two possibilities exist:
[A21 II., 2 ?I,,
[A21C II., < ?i,.
Hence, [A21 implies that ii,,, > II., 2 n, > II,, whereas
[A2] implies ni, > n, > II., > II,. This can be
interpreted as a condition on (1) *how the two types differ as well
as (2) how the industrial structure affects the incumbent profits.
Since [A21 states that monopoly profits are higher for each type,
we can view this as a situation where the type difference is less
signil%ant than the difference in the industrial structure. Under
[A21C, since the high type profits
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M. N, Durrough and N. hf. Stoughton, Entry andjnanciaf disclawe
225
are higher regardless of the industrial structure, this is a
situation where the type difference is more significant6
Our intuition suggests that when the type difference is more
significant, the motive for type H to be evaluated correctly by the
financial market outweighs the motive for preventing entry. This
encourages disclosure. Type L is subject to different motives. They
would rather hide their information, in which they might succeed if
they choose nondisclosure. (Of course, they would be success- ful
only if the H type also followed a nondisclosure policy.) When the
industrial structure is more important, prevention of entry becomes
the crucial consideration. The L type reveals itself to discourage
entry, whereas the only hope for H is through nondisclosure. Our
main results in the next sections rely on [A21 (as a sufficient
condition). To be complete, we also present a discus- sion on the
implications of [A21c.
The third assumption guarantees that at least the incumbent will
remain in the industry even under unfavorable conditions. Moreover,
this assumes that the investment opportunity always has positive
net present value in a world of complete information:
[A31 fi,>I7,> K>O.
Finally, we make the following important assumption:
[A4] Disclosure is truthful and costless.
The truthful disclosure assumption simplifies our analysis and
is common to most disclosure models. It is reasonable if the
disclosed information is audited or verifiable. *s It is also a
necessary condition to get existence of a full disclosure
equilibrium in our model.
This also implies that a game-theoretic analysis predicated on
[AZ] may not be robust with respect to an increase in the number of
types. Specifically, [A21 may be indicative of what one would get
in a model with a continuum of types.
If disclosure cannot be credible, then the firms may attempt to
communicate their type through other signals such as capital
structure.
*If disclosures require a fixed amount of administrative costs,
then firms will not be indifferent between disclosure and
nondisclosure when they are identified anyway. Type H in
Proposition 1 will strictly prefer nondisclosure to disclosure. The
nature of tradeoffs and equilibria, however, is not at&&xl
by the assumption of a fixed disclosure cost.
91t can be shown that [A41 is not needed in the following
circumstanoe. If [AZ) holds and the intrinsic value of a H type
firm that falsely declares low is depleted by the amount of the
misrepresentation, then outright lies become dominated strategies
for the incumbent types.
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226 M. N. Durrough and N. M. Stoughton, Entry and financial
disclosure
2.3. Definition of strategies
Disclosure policy for the incumbent is defined aslo
d, =s(d=HIH), d,=B(d=LIL),
where d, (d2) represents the probability that disclosure is made
given that the incumbents private information is H (L).
Entry policy of the entraint is
e=P(entryId=ND),
where e represents the probability of entry when no disclosure
was made. Assumptions [Al] and [A41 imply that the potential
entrant will enter when d = H and will not enter when d = L with
probability one. The structure of beliefs by the two parties is
denoted by
p=9(H), q=g(Hld=iVD),
where p, 0 -C p -C 1, is the prior belief and q is the posterior
belief of the financial market and the entrant upon observing no
disclosure. Again the assumption of truthful disclosure implies
that the posterior beliefs must be that the incumbent is type H
when d = H and type L when d = L. The extensive form of the game is
given in fig. 1 along with profits for incumbent and entrant
(without explicit depiction of the financial market). Note, how-
ever, that Zs profit represents (actual) intrinsic value (and not
the payoff function).
3. Strategic analysis
The equilibrium concept we employ is sequential equilibrium due
to Kreps and Wilson (1982). The game is defined by the extensive
form in fig. 1 plus the common knowledge information, p, the prior
belief of the financial market and the entrant as to the type of
the incumbent. Using the definitions contained in the previous
section regarding entry and disclosure policy, a sequential
equilibrium is defined by
(d,,d,,e,q}.
Furthermore, the posterior beliefs in the information set must
satisfy the Bayes consistency requirement as long as the
denominator of the following
9 denotes probability.
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M. N. Durrough and N. M. Stoughton, Entry and financial
disclosure 221
Dimehum Policy
Entrants
Policy
Ir Proa Er Pro5t
(Actual) (Actud)
Fig. 1. Extensive form.
expression is positive:
Al - 4) q = T(l - d,) + (1 -p)(l -d*) . (1)
In order to determine the set of sequential equilibria, first we
investigate the entrants best responses conditional on their
beliefs. We then analyze the incumbents disclosure strategy {d,,
d,} as a function of the entrants entry response function and
financial market valuation. Results are then combined to find
necessary conditions on the common knowledge parameters that
support the various types of equilibria and on endogenous beliefs,
q.
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228 M. N. Dorrough OIK/ N. M. Stoughron, Entry ondjnoncioi
oYsciloure
3. I. Entrants strategy
If entrants observe a favorable disclosure, d = H, they will
enter for sure, while they will stay out upon observing d = L. This
is due to the assumption that disclosure is always truthful and
that the entrants actual profit is positive only when the market
condition is favorable, [Al]. When the incumbent does not disclose,
however, the entrant policy depends upon the expected payoffs,
E(n,lQND), where ad, d E {D, ND}, is the information set with s2*
repre- senting information with disclosure and QND without
disclosure. Entry takes place if the expected profit is strictly
positive, i.e.,
or
(2)
where 0 < p < 1 using [Al]. The value of p can be
interpreted as the relative cost of entry.
In summary, the entrant strategy is as follows:
e=l * 4PcL,
e=O = q
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M. N. Darrough and N. M. Stoughton, Entry and jnancial dischue
229
E(Z7,lP, e), the expected profit of the incumbent conditioned on
the inforrna- tion set and entry policy. M aximization of
shareholder value amounts to multiplying the retained ownership
fraction, 1 - (Y, times the intrinsic expected profit from the
informed incumbents point of view, E(If,la, e), D E {H, L}.
Therefore the objective is
When disclosure is truthful, the objective function can be
simplified since
K
- E( II,lP, e) E(fl,lfi, e) = E(fl,lQ, e) - K,
when d = D. Moreover, if the incumbent follows a pure disclosure
strategy, then it is simple to compute the actual payoffs of the
game. Any complication in analyzing the game, therefore, arises
from the possibilities of nondisclosure as well as mixed
strategies. Since the entrants strategy depends on the posterior,
the incumbents strategies must be analyzed for each posterior (upon
no disclosure) in order to derive all the potential equilibria.
Given the entrants strategy and the financial markets rational
expectations, the incum- bent decides whether to disclose. Benefits
and costs of disclosure depend upon the private information (or
type). These are as follows:
For H, disclosure will identify their type, inducing entry as
well as correct valuation. Thus, incumbents will receive
TI,- K, (6)
the profit from the duopoly game minus the portion of the firm
sold to the new shareholders. If they choose not to disclose, then
they will be valued in a pooled fashion, i.e.,
e l-; ?i,+(l-e) l--F.I?,, i 1 ( 1
where
If the net benefit is positive, (6) greater than (7), then H
will disclose.
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230 M. N. Durrough and N. M. Stoughton. Entry and financial
diselapure
The same logic applies to L. The benefit from disclosure is
prevention of entry, resulting in the monopoly profit of
&f--K, (8)
while by not disclosing they would be pooled as in (7). In other
words, nondisclosure gives both types the same market valuation,
but disclosure has different benefits. Whether or not disclosure
takes place depends on whether or not net benefit is positive.
Under assumption [A2], II, > ?I,. This implies that if both
types disclose in equilibrium, the low type has a higher monopoly
profit than the high type as a duopolist.
4. Equilibrium
We now examine equilibria of the game. The following analysis is
based on the assumption that [A21 holds. As discussed earlier, this
is a situation in which the type difference is not as significant
as the difference in the industrial structure. Three types of
equilibria are identified: (1) both types disclose when the costs
of entry are low and/or the prior is relatively optimistic; (2)
neither discloses when the prior is relatively pessimistic and/or
the entry costs are high; and (3) in addition, there is a mixed
strategy equilibrium under the same conditions as (2). When both
types disclose, their types are clearly revealed. This kind of
separating equilibrium is referred to as a disclosure equilibrium.
The second equilibrium is called a nondisclosure equilibrium. We
start our discussion with the disclosure equilibrium.
Proposition I. Under assumption [AZ], there exists a set of
sequential equilibria that are observationally equivalent to a
disclosure equilibrium in which both types disclose. Entry occurs
for certain in the event of ND. Symbolically,
{d,E[0,1],d2=1,e=1}.
Moreover, when p > u, this is the unique sequential
equilibrium outcome.
Proof. The proof shows that these constitute best responses of
the players given the equilibrium strategies of the other players.
In addition, they must be sequentially rational. We can show that a
consistent belief is q = 1. This requires showing that both types
of incumbent prefer disclosure, when e = 1 and the financial market
reacts rationally.
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M, N. Durrough and N. M. Sloughton, Entry andjinancial disclawre
231
If the incumbent is of type L, I still prefers disclosure if
expected profit from disclosure is higher than that under a
nondisclosure policy, i.e.,
where
= n,. (10)
The left-hand side of (9) represents the expected profit when d
= L, whereas the right-hand side represents the expected profit
when d = ND. Rewriting the inequality, we obtain
This may be rearranged to yield
(11)
Given [A2], a,., 2 n, is sufficient for (II, - &)/(fi, -
II,) 2 1, which in turn implies the above inequality in conjunction
with [A3]. In fact, the low type strictly prefers to disclose.
If the incumbent is of type H, then disclosure is followed by
certain entry. Hence this type of incumbent is indifferent between
disclosure and no disclo- sure with e = 1. This supports the
proposed equilibrium.
In addition, it can be shown that posterior beliefs p < q
< 1 are also consistent with the disclosure equilibrium where d,
= 1, since the high type has a strict incentive to disclose in this
case. (If the high type chose ND, then valuation would be less but
there would still be a certainty of entry.) With the above beliefs,
the low type still prefers disclosure. This is because under [A2],
we have just shown that the low type prefers disclosure when ND
prompts valuation as the high type; hence lower valuation cannot
make the low type better off. Finally, the uniqueness question must
be addressed. This follows from the following three propositions
which collectively verify that if [A21 holds, the only other
sequential equilibria require p 5 p. l
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232 M. N, Durrough and N. M. Stoughton, Entry andjinancial
disclosure
The disclosure equilibrium above is supported by a prior that is
optimistic compared to the relative cost of entry, p. Notice that
Proposition 1 identifies an equivalence class of equilibria in that
the type always is identified. That is, although the set of
equilibrium actions is nonunique, the equilibrium outcome is
nevertheless unique. * When both d, = d, = 1, Bayes theorem cannot
be applied. However, this equilibrium point is connected to the
strictly random- ized points, which imply that posterior beliefs
are that the type is high upon nondisclosure. This means that the
equilibria in Proposition 1 are part of a stable set as Kohlberg
and Mertens (1986) have defined; furthermore, refine- ments such as
the intuitive criterion [Cho and Kreps (1987)] and universal
divinity [Banks and Sobel(1987)] will never eliminate the
disclosure equilibria. Since the disclosure equilibrium is the only
potential equilibrium where there is freedom to choose
off-equilibrium beliefs, these refinement concepts are powerless in
our model with respect to eliminating multiple equilibria. The
equilibrium requires that q > cc, implying that the posterior
must be optimistic but no restrictions are imposed on the prior.
Since there could be other equilibria when p I CL, the disclosure
equilibrium uniquely obtains when p > p. This disclosure
equilibrium is robust under assumption [A2].
An interesting. market reaction is implied under [A21 in the
disclosure equilibrium. For a type L firm, since the disclosure
prevents entry, the market values the firm as 0,. For a high type
firm, the market values the firm as n,. Under [A2], these ex post
values are & 2 ?I,, so that the price response to unfavorable
information involves an increase, while prices decrease when
favorable information is disclosed.
When the market is pessimistic, however, the H type may decide
not to disclose since this discourages entry. The L type may also
find it advantageous not to disclose, since it does not have to
worry about discouraging entry (by disclosing its L type) and can
hide behind no disclosure to obtain better financing terms by being
pooled with the high type. Thus, we can have the following
equilibrium:
Proposition 2. Given [AZ], there exists a nondisclosure
sequential equilibrium in which both types choose not to disclose
if and only if p < PL:
{d,=O,d,=O,e=O}.
Proof. Clearly the nondisclosure equilibrium requires that prior
beliefs equal posterior beliefs. To support no entry implies that p
= q < c. Given e = 0, the
12Such multiplicities are innocuous. For example, they are also
present in the models of Grossman (1981) and Milgrom (1981).
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M. N. Durrough and N. M. Stoughton, Entry andfinancial
disclosure 233
high type of incumbent prefers ND if
i i l-f n,rn,-K.
This can be rearranged to give the equivalent condition
02)
Assumption [A21 implies that i?, 5 Q,,, < V, so that
assumption [A31 is sufficient to imply (12). Since entry will not
occur for the low type upon disclosure, this type benefits from
higher financial market valuation. Choosing ND is therefore
consistent with sequential rationality. n
For type H, discouraging entry (by providing no information) is
more important than being correctly evaluated by the financial
market. Of course, the H types cannot differentiate themselves from
the L types. The L types are definitely better off, since they
receive higher valuation by the financial market, and face no
possibility of entry - the L types are free-riders here. Given the
no-disclosure policy of the two types, {d, = 0, d, = 0}, the
entrant and the financial market update their prior as
= ~(1 - d,) + (1 -p)(l - d2) =*
which shows that the entrants pessimism originates from their
prior as to the incumbent type. When the market and the entrant do
not suspect that the incumbent is likely to have favorable news,
the H type would rather hide behind the veil of pessimism.
What kind of equilibrium could obtain when the posterior is
totally pes- simistic, or q = O? Then, since no disclosure
discourages entry for sure, even the H type is willing to forgo
correct evaluation from the financial market, as in the last case.
On the other hand, since no entry takes place whether they disclose
or not, type L will be indifferent between disclosure and no
disclo- sure. It might appear that {d, = 0, d, E (O,l)} is a
potential equilibrium. However, this is not sequentially
consistent, since q cannot be zero given these disclosure
policies.
Propositions 1 and 2 considered the cases where q > p and q
< p, respec- tively. We are left with the situation when q = p.
This is a case in which the entrant might pursue a mixed strategy
upon observing no disclosure, since the expected value of entry is
zero. It can be shown that an equilibrium exists in
-
234 M. N. Dmrough and N. M. Stoughton, Enty andfiMncia1
disclosure
which one type of incumbent randomizes and the other does not
disclose. It is not possible to have an equilibrium in which one
randomizes and the other discloses, since in that case q would have
to be zero or one, which is a contradiction to the hypothesis of q
= p.
Proposition 3. Given [AZ], there exists a partial disclosure
equilibrium in which the high type chooses not to disclose, the low
type randomizes and entry is random when nondisclosure is observed
if and only if p < p, i.e.,
i d, = 0, d, = (l:;,p, e = e* E (0,l) .
I
Proof. To support this mixed strategy equilibrium, the posterior
beliefs upon nondisclosure must leave the entrant indifferent. That
is, q = ~1. Since in this proposed equilibrium only the incumbent
with favorable information always chooses nondisclosure, the
posterior belief, q, must be larger than the prior, p. This yields
the necessary condition that p > p. Notice that when d, = (p -
p)/(l - p)~, the posterior belief computed using Bayes rule is
P =
P + 1 - (lp_-;)ll (1 -P) i i
El,
as indeed it should be. Let e* denote the entry probability. The
valuation of the financial market
after observing nondisclosure is then
v=e*(Q,+p(Ti,-l7,)) +(l -e*>(!Lf+P(nh4-hf))*
Since the L type incumbent is indifferent between disclosure and
nondisclo- sure, the entry probability must be such that
l&-K= l-5 (e*aI+(l-e*)a+,). i 1
(13)
We claim that if [A21 is satisfied, there always exists an e* E
(0,l) such that equality in (13) is achieved. To verify this claim,
note that if e* is one, then the left-hand side of eq. (13) is
greater than the right-hand side:
i
K &J-K l- n,+,(j=j,-Q,) n19
1 (14)
-
M. N. Darrough and N. hf. Stoughton, Entry andjinancial
disclosure 235
using [A2]. On the other hand, if e* is zero, then the left-hand
side of (13) would be less than the right-hand side since
By continuity of the right-hand side of (13) there exists an e*
E (0,l) such that (13) holds.
Now, we must verify that at e*, the H type strictly prefers
nondisclosure to disclosure. That is,
?f,-K< l-; (e*n,+(l-e*)?i,). i 1
05)
= 1 - f (e*III+ (1 - e*)II,) i i
c 1 - ; (e*fi,+ (1 - e*)?I,), i 1
which proves the result. The first inequality above follows from
[A21 and the equality comes from eq. (13). H
Notice that in this equilibrium, revelation of the type does
take place with positive probability. Thus when the low type
happens to disclose, entry would not ensue. When nothing is
disclosed, however, entry might or might not occur.
4.1. The financial market and [A2]
When [A21 does not hold, the above results are essentially
unchanged as long as the amount of external financing required, K,
is relatively small. We outline below how this claim can
be.demonstrated in the above propositions.
With respect to the disclosure equilibrium (Proposition l), the
key is that the low type should not prefer ND and the consequent
higher valuation. A necessary condition for this is eq. (11). In
this case, even if [A21C holds so that (&- II,)/(fi, - II,)
< 1, this is bounded away from zero so that (11) can still be
satisfied for low values of K.
-
236 M. N. Durrough and N. M. Stoughton, Entry andjnancial
disclosure
Similar logic applies to Proposition 2. Here the critical
incentive compatibil- ity condition is (12). Once a@n, the
right-hand side is strictly positive since V < n, even though
&, < l7, when [A21C is true. Therefore, the nondisclo- sure
equilibrium will still exist when the external financing
requirement is sufficiently small.
For the mixed strategy equilibrium of Proposition 3, the results
are similar. Again the equilibrium will exist in the absence of
[A21 if K is suitably chosen. It can be seen that as K tends toward
zero, the low type has to be indifferent, which causes the
equilibrium entry probability, e*, to approach zero. But this
lowering of the chance of entry encourages the high type to select
nondisclo- sure and tends to uphold the equilibrium.
The intuitive argument for why the assumption of [A21 and low
values of K leads to similar predictions runs as follows. In the
disclosure equilibrium, the binding constraint is that the low type
should resist the temptation of garnering excessive financial
market value at the expense of incurring entry. Under [A2], the
relative valuation gains are limited by the favorable position of
the low monopolist vis-&is the high duopolist. Alternatively,
the potential valuation gains can be limited by a modest external
financing requirement. In the nondisclosure equilibrium, the
binding constraint is that the high type should discourage entry by
pooling with the low type. This requires the acceptance of some
amount of underpricing by the financial market. When [A21 holds,
the underpricing is limited by the favorable position enjoyed by
the low type monopolist. Alternatively, the disutility due to
underpricing might be limited by a small magnitude of external
financing.
Another sufficient condition for the simultaneous existence of
full, non, and partial disclosure equilibria is that the incumbent
and the entrant be similar. In a Coumot or Stackelberg duopoly
game, if there are homogeneous products and identical costs, then
it is easily shown that the bounds on K implied by (ll), (12) and
(14) are larger than II,. Thus, by [A3], the above equilibria
exist. The reason for this is that a very different entrant (e.g.,
low coefficient of differentiation) implies that the profit of the
incumbent is affected relatively less by entry, and hence the
threat of entry is not as important. The incumbent then will care
more about financial valuation than entry deterence - a similar
situation to K being large.
What happens when the equilibria of Propositions l-3 do not
exist? Although we believe that the economic environment required
for Propositions l-3 is more relevant, for the sake of
completeness, a brief discussion is provided on alternative
equilibria. Interestingly enough, even when K is large and [A21C is
satisfied, there is existence of full disclosure. The following
proposition gives this result:
Proposition 4. Suppose that [AZ] hola!s and K is suficiently
large. Then there exists a disclosure equilibrium in which the high
type discloses and the low type
-
M. N. Darrough and N. M. Stoughton, Entry andjinancial
disclosure 231
randomizes. Upon nondisclosure, the entrant stays out, i.e.,
{d,=l,d,E[O,l],e=O}.
Proof. The low type is clearly indifferent between disclosing or
not. Since only the low type ever chooses nondisclosure, posterior
beliefs can be q = 0, which supports the decision not to enter. We
only need to show that the high type prefers to disclose. This is
so if
This is equivalent to
It is easy to see that this holds only if K is sufIiciently
large and [A21C is satisfied. n
This proposition yields an equilibrium that is observationally
equivalent to that of Proposition 1. In both cases, the types are
identitied and the entrant enters if and only if information is
favorable. Hence, full disclosure exists either when [A21 is
satisfied or the importance of the financial market is significant.
When [A2] is true but K is in some intermediate range, full
disclosure does not exist. When the market is optimistic, we can
have a fourth type of equilibrium involving a random disclosure
policy by the high type and no disclosure by the low type. Entry is
also random following nondisclosure. It can be shown again that
this equilibrium exists only if [A21 is not satisfied and K is
sufficiently large. Only favorable information is ever
disclosed.
Proposition 5. A sequential equilibrium involving the
strategies:
d = - 1 Pk-!4*
d,=O, e=e^E(O,l)
exists if and only if p > ~1, [ A21C hol&, and K is
suficiently large.
06)
Proof. The requirement of posterior beliefs in this equilibrium
is that p > IL, since the high type is mixing and the posterior
beliefs must satisfy q = p. It is easily verified that the
randomization probability prescribed above accom- plishes the
desired effect through Bayes rule.
-
238 M. N. Durrough and N. M. Stoughton, Entry and financial
disclasure
We now demonstrate that this equilibrium cannot exist under
[A2]. Denote the convex combination of monopoly and duopoly profits
of both types as
?I=li,C+(l-e^)?l,, a= I&s+ (1 - Z)l7,.
Then to support this equilibrium, we require as necessary
that
holds for the high type, where V is the valuation given
nondisclosure. At the same time, the low type must have an
incentive not to disclose so that
(17)
Suppose that [A21 is satisfied so that II, 2 ?Tr. Applying this
to the two previous equations we arrive at the conclusion that
But this implies that a 2 n which is a contradiction. When [A21C
holds, we can also derive a contradiction when K is
sufficiently
small. The argument is as follows. Consider the indifference
relation of the high type. As K tends to zero, the probability of
entry, P, must go to one. This causes Q + II,. But then the
incentive compatibility condition given by eq. (17)
failsbY&ause l7, < &. n
The intuitive explanation is as follows. The low type has to
strictly prefer nondisclosure with the concomitant probability of
entry. In order for this to be the case, the low type must be
compensated by higher valuation in the event of nondisclosure. But
if the types are close so that [A21 is satisfied, then the high
type will switch to nondisclosure. This occurs because
undervaluation is relatively unimportant given that entry is
induced for sure upon disclosure, but only randomly upon
nondisclosure. Hence the potential equilibrium is broken.
5. Discussion and conclusion
Under a condition which amounts to entry deterrence being more
important than financial valuation, we have identified three
equilibria in the disclosure
-
M.N. Darrough and N. M. Stoughton, Entry and financial
disclosure 239
game: (1) a disclosure equilibrium in which both types disclose
their types when the prior is optimistic or the entry cost is
relatively low; (2) a nondisclo- sure equilibrium in which neither
type discloses when the prior is relatively pessimistic or the
entry cost is relatively high; and (3) a partial disclosure
equilibrium in which only unfavorable information is ever
disclosed. In the disclosure equilibrium, we also document the
interesting effect that market price reactions can be inversely
related to the announcement of favorable or unfavorable news. The
entrant enters, however, if and only if the incumbent is revealed
to have favorable information. Entry probability, therefore, is
exactly the same as under full information. No entry deterrence
takes place in equilibrium. The equilibrium then would be
considered socially desirable. Since disclosure of proprietary
information is made voluntarily, this suggests that mandatory
requirements for disclosure are not necessary in this case. There
appears to be a role in the accounting profession in facilitating
truthful disclosures through auditing to prevent falsehood.
When the prior is pessimistic relative to the cost of entry,
since the threat of entry is weak, firms might not disclose. Upon
no disclosure, the entrant is deterred from entry. This happens
regardless of the nature of underlying private information.
Although the prior is relatively low, even socially desir- able
entry is prevented. Obviously the incumbent monopolist is better
off, but consumers and the potential entrant lose out. This result
can be used as a justification for a mandatory disclosure
requirement of proprietary informa- tion. It might also provide a
justification for the existence of private place- ments, as
Campbell (1979) has observed.
An important implication of our model is that competition
through threat of entry encourages voluntary disclosure.
Verrecchia, on the other hand, sug- gested that the less
competitive industries are, the more disclosure takes place. The
source of differing conclusions appears to be the interpretation of
compe- tition and costs.13 In our paper, the question of obtaining
a unique full disclosure equilibrium depends on the relative entry
costs. We conclude that since low entry costs leads to a higher
entry probability, full disclosure ensues under competitive
pressure. By contrast, consider a model in which there is a set of
rivals to an informed firm who have already entered. Then, the cost
of disclosure to an informed firm with favorable information is
that it will induce the rivals to produce more. It is possible that
as the size of the set of rivals increases, disclosure becomes more
costly. If competitive situations are associ- ated with greater
numbers of rivals, then such a model might yield the prediction
that competition discourages voluntary disclosure. This might have
been what Verrecchia had in mind when he adopted the premise that
the proprietary costs of disclosure are greater in more competitive
situations. In both Verrecchias as well as our model, less
disclosure is associated with higher
l3 We appreciate Ro Verrecchia for bringing this to our
attention.
-
240 M. N. Durrough and NM. Stoughton, Entry andjnancial
disclosure
costs. The different predictions can be traced to the ways in
which competition affects the respective cost definitions.
The detailed model of the appendix assumes a standard Coumot
duopoly structure. Although this is not the only possible duopoly
solution, it is a reasonable one in our simultaneous move game.
Other models are possible, however. For example, the firms might be
engaged in Bertrand competition (price choice). In order to deter
ent_ry, the incumbent could choose a low price. In the simultaneous
setting, however, there is no way that the incumbent can signal
their intention of flooding the market (unless this is incorporated
in the disclosure mechanism as a policy choice); moreover this
threat may not be even credible (not subgame perfect).
Alternatively, the incumbent could at- tempt to be a Stackelberg
leader. The incumbents profit as a duopolist would then be higher
than as a Coumot duopolist. The level of profits is affected, but
the analysis of equilibrium would not be. The incentive for
deterrence is lessened. but the basic tradeoffs are still the
same.
Appendix
A. I. A Cournot duopoiy game with diferentiated products
For illustration, we work out the comparative statics in the
case of a Cournot game with linear demand and cost. Assume that the
incumbent is faced with an inverse demand function for its product
of the form:
Pi=a-b(Qi+tQi), 08)
where Pi, i = Z, E, are the prices; Qi and Qj, j = E, I, are the
quantities sold; and 0 I t I 1 is the coefficient of
differentiation. If t = 1, then we have perfect substitutes
(homogeneous products).
Given this demand, the incumbent (variable) profit is
when the marginal cost of production, c, is assumed to be
constant. If the incumbent remains as a monopolist, then its
profit-maximizing output is Q,,, = (a - cM2b). l4 The corresponding
monopoly profit is 17, = (a - c)*/(4b).
As long as a > c, the output and profit are strictly
positive, thereby creating an inducement for entry by the potential
entrant. If entry does take place, then
14Based on a simple behavioral assumption that the monopolist
chooses the quantity (price) that maximizes his profit, taking QE =
0. This behavior may not be optimal if the order of moves is
reversed and the entry decision is made subsequent to quantity
setting. For example, limit pricing models examine the incentive of
the monopolist incentive to cut price to discourage entry.
-
M, N. Durrough and N. M. Stoughton, Entry and financial
disclosure 241
the market is shared. In the case of a Cournot-Nash duopoly
game, the equilibrium outputs are
Q,= 2(u - c) - t(a - CE)
b(4- t2)
and QE=2b-+t(4 b(4-t2)
where cE is the entrants marginal cost. For the outputs to be
strictly positive, we assume that 2( a - c) - t( u - cE) > 0 and
2( a - cE) - t( a - c) > 0. Special cases of interest would be:
(1) when c = cE and (2) when c = ?, and t = 1. Then, Q, = QE = (a -
c)/b(2 + t) and Q, = QE = (a - c)/3b, respectively.
Substituting optimum quantities to derive the equilibrium prices
allows us to calculate Coumot equilibrium (variable) profits for
the two firms (before any fixed cost or cost of entry):
~ I
= &J-c)-r(a-c,)j2 b(4 - t)
and
II E
= {2(-,)-~b-c)j2 b(4-t2)2 .
09)
To see how the entry incentive of the potential entrant is
affected, it is useful to examine comparative statics of the above
equilibrium. For example, we show that an increase in the value of
the demand intercept will raise the equilibrium profits of both
duopolists. To see this, totally differentiate (19) and (20) with
respect to a. Using the envelope theorem,
dn, _ 2{2(a-c) 4--c,)) >. da b(2 + r)(4 - P)
and
dn, 2{2(u - CE) - t(u - c)} -= da b(2 + t)(4 - P)
> 0.
Similarly it is straightforward to show that the slope of the
demand curve and the coefficient of differentiation affect the
profits of duopolists in the same direction. That is, the flatter
the demand curve (the lower the value of b), the higher the
profits. The more differentiated the products are, the higher the
profits. This latter comparative static requires the assumption
that parameter
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242 M. N. Durrough and N. M. Stoughton, Entry and financial
disclosure
values satisfy
a(2-t)+4ct cE < 4+t2
when c 5 cE.
A.2. [A21 versus [A2]
It is possible to compare the implications of the two
alternative assump- tions, once we have the profit levels for the
incumbent and entrant as (19) and (20). The assumption [A21 states
that II,, 2 lI,, implying that the low type monopolist has a higher
profit level than the high type under duopoly. This is a result of
two factors: (1) industrial structure and (2) type difference.
Given equations for II,+, and (19) it is simple to compare various
profit levels. Since 2( a - c) - t( a - cE) > 0, we can compare
the profit levels by comparing
a-c
26 I. and 2b7-44~-C,)
(4-12)& H
For example, suppose a is the private information of the
incumbent. Assume a E {a, a> and a = g + A. Simple algebra shows
that
This simplifies to a condition that A I (a - c)/2 when t = 1 and
c = cE. The type difference cannot be too big, given the Coumot
duopoly structure. If the firms played a different duopoly game,
the bound on the type difference changes. For example, if the
incumbent is a Stackelberg leader, then its profit in the duopoly
game is higher than that under Coumot game. Therefore, the bound on
type difference would be smaller.
A similar result obtains with respect to b. Let b E { _b, b} and
6 = hfi. Then: .-.
&,>?1, * hs (fl- ?)(a - c)
4(a-c)-2t(a-c,)
If c = cE and t = 1, then this simplifies to h 5 :. The
situation is different for t, however. Since the best possible
parameter
value is t = 0 (total independence), for any value t > 0, the
duopolists have to
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M. N. Out-rough and N. M. Stoughton, En@ andjinancial disclosure
243
share the market. Profit is strictly lower for the duopolist
incumbent regardless of demand or cost conditions as long as t >
0. Therefore, [A21 holds strictly in this case.
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