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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 firm’s value more accurately; the disclosure, however, could compromise the incumbent’s 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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  • 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)

  • 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).

  • 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

  • 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.

  • 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.

  • 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

  • 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.

  • 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.

  • 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.

  • 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

  • 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.

  • 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.

  • 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

  • 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).

  • 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

  • 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

  • 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.

    References

    Ambarish, R., 1988, Threat of entry, strategic entry deterrence and signaIling in financial markets, NYU working paper.

    Banks, J. and J. Sobel. 1987, Equilibrium selection in signahng games, Econometrica 55,647-661. Bhattacharya, S. and J.R. Ritter, 1983, Innovation and communication: Signalling with partial

    disclosure, Review of Economic Studies 50, 331-346. Campbell, T.. 1979. Optimal investment financing decision and the value of confidentiality,

    Journal of Financial and Quantitative Analysis 14, 913-924. Cho, I. and D. Kreps, 1987, Signalling games and stable equilibria, Quarterly Journal of

    Economics 102, 179-221. Dye, R.A.. 1985a, Disclosure of nonproprietary information, Journal of Accounting Research 23,

    123-145. Dye, R.A., 1985b, Strategic accounting choice and the effects of alternative financial reporting

    requirements, Journal of Accounting Research 23.544-574. Dye, R.A., 1986, Proprietary and nonproprietary disclosures, Journal of Business 59,331-366. Gal-Or, E.. 1985, Information sharing in oligopoly, Econometrica 53, 329-343. Gal-Or, E., 1986, Information transmission - Coumot and Bertrand equilibria, Review of Eco

    nomic Studies 53, 85-92. Gertner, R., R. Gibbons. and D. Scharfstein, 1988, Simultaneous signalling to the capital and

    product markets, Rand Journal of Economics 19,173-190. Grossman, S., 1981, The informational role of warranties and private disclosure about product

    quality, Journal of Law and Economics 24.461-483. Harrington. J., 1986, Limit pricing when the potential entrant is uncertain of its cost function,

    Econometrica 54.429-437. Hughes, P.J., 1986. Signalling by direct disclosure under asymmetric information, Journal of

    Accounting and Economics 8, 119-142. John, K. and J. Williams, 1985, Dividends, dilution, and taxes: A signaIling equilibrium, Journal

    of Finance 40, 1053-1070. Kohlberg, E. and J.F. Mertens. 1986, On the strategic stability of equilibria, Econometrica 54,

    1003-1037. Krcps, David and Robert Wilson, 1982, Sequential equilibrium, Econometrica 50, 863-894. Milgrom, P., 1981, Good news and bad news: Representation theorems and applications, Bell

    Journal of Economics 12,380-391. Milgrom, P. and J. Roberts, 1982, Limit pricing and entry under incomplete information: An

    equilibrium analysis, Econometrica 50,443-459. Miller, M. and K. Rock. 1985. Dividend policy under asymmetric information, Journal of Finance

    40,1031-1051. Verrecchia. R.E.. 1983, Discretionary disclosure, Journal of Accounting and Economics 5.179-194. Vives, X.. 1984. Duopoly information equilibrium: Coumot and Bertrand, Journal of Economic

    Theory 34. 71-94.