Disclosure Regulation in Duopoly Markets: Proprietary Costs and Social Welfare

Abstract

The argument of proprietary costs is commonly used by firms to object against proposed disclosure regulations. The goal of this paper is to improve our understanding of the welfare consequences of disclosure in duopoly markets and to identify market settings where proprietary costs are a viable argument for firms to remain silent. We, therefore, solve the optimal disclosure strategies and distinguish two different potentially costly effects of disclosing private information: the strategic information effect and the market information effect. We identify the market settings for which a regulator prefers to impose disclosure regulation so as to maximise consumer surplus or total surplus. Regulation may be necessary because (i) the increase in welfare outweighs proprietary costs to the firms, or (ii) firms are trapped in a prisoners' dilemma. The first primarily applies to Bertrand competition with demand uncertainty and, to a lesser extent, to Cournot competition. The second applies primarily to Cournot competition and Bertrand competition with cost uncertainty.

Acknowledgements

The comments and suggestions made by Christian Hofmann (associate editor), two anonymous reviewers, Silviu Glavan, Teye Marra, Eelke Wiersma and participants of the 2009 Accounting Research Workshop in Bern are gratefully acknowledged.

Notes

¹Examples of accounting studies that take proprietary costs of disclosure as exogenous are Verrecchia (1983) and Dye (1986). Endogenous proprietary costs are considered in, amongst others, Wagenhofer (1990) (single firm setting) and Darrough and Stoughton (1990), Feltham and Xie (1992), Hughes et al. (2002) and Arya et al. (2010) (multiple firm setting). For an extensive survey of disclosure models in accounting, see Verrecchia (2001), Dye (2001), and Beyer et al. (2010).

²See, for example Vives (1984), Gal-Or (1985), Gal-Or (1986), Raith (1996), and Vives (2002).

³A related study by Corona and Nan (2011) also focuses on welfare issues in duopoly settings. This study shows that firms may over/underinvest when they can preannounce their quantity/price decisions. Other related studies include Arya et al. (2010, 2011) that focus on the source of proprietary costs, and Evans and Sridhar (2002), Fischer and Verrecchia (2004), Rothenberg (2009), and Bagnoli and Watts (2010) that focus on the credibility of firm disclosures.

⁴See, for example Vives (1984), Gal-Or (1985), Gal-Or (1986), Darrough (1993), Vives (2002), Hughes and Williams (2008), and Bagnoli and Watts (2010).

⁵The information structure in Darrough (1993) corresponds to the special case r = 1 where demand parameters for product 1 and 2 are identical. Identical demand parameters is also commonly assumed in the information sharing literature (Gal-Or 1985; Vives 1984, 2002) Observe that the information structure used in this paper is a special case of the information structure considered in Bagnoli and Watts (2011). That study, however, only focuses on the disclosure decision of the firm and does not analyse the effects on social welfare.

⁶Formally speaking, r does not equal the correlation between demand parameters α₁ and α₂ as . However, it holds that Corr [α₁, α₂] is increasing in r for and Corr [α₁, α₂] equals −1, 0, 1 for r = −1, 0, 1, respectively.

⁷In contrast, Raith (1996) considers correlated demand intercepts in a different information structure. Raith (1996) assumes that α_i and α_j are jointly normally distributed with correlation coefficient r. Furthermore, each firm i receives a noisy signal of α_i, that is with ϵ_i and ϵ_j jointly normally distributed. However, the complexity of this information structure confines the analysis in Raith (1996) to three special cases, namely, (i) identical demand parameters (i.e. α_i = α_j), (ii) independent private information (i.e. ϵ_i and ϵ_j are uncorrelated), and (iii) perfect private information (i.e. , i = 1, 2).

⁸The assumed normal distributions of , and ρ_i may yield negative quantities , which should be infeasible in our duopoly setting. We assume, however, that mean and variance parameters of these probability distributions are such that negative quantities are highly unlikely and will not affect a firm's disclosure decision. Henceforth, we ignore the possibility of negative quantity (or price) choices. Previous studies on oligopolies with uncertainty make similar assumptions (cf. Darrough 1993, and others).

⁹The proof is in the appendix.

¹⁰Our definition of the consumer is similar to existing research (cf. Vives 1984, 2002) and consistent with the usual interpretation that the consumer surplus is determined by the area enclosed between the inverse demand function and the actual price. To see this, observe that in case of no uncertainty, the usual interpretation of the consumer surplus yields , which is equal to .

¹¹We thus focus on a social welfare measure and do not discuss whether a regulator will indeed act in line with this objective. This analysis thus takes the public interest theory, where the regulator acts in line with the public interest, as perspective on the regulator. The regulator may in reality make different decisions, e.g. in line with its own objectives and/or based on lobbying (interest group theory). For more on the theories of regulation, we refer to Posner (1974).

¹²The other two combinations of regulator preference, firm preference, and strategic equilibrium would consist of a strategic equilibrium where firms play full disclosure, while they prefer non-disclosure, which never occur in our setting.

¹³For the case of complements, consumers benefit from negatively correlated supplies. This may seem counterintuitive as for complementary products, consumer utility depends on the consumption of both products. Positively correlated supplies, however, drive up the prices for both products, which in turn negatively affects consumer utility. Again, firms use their disclosure policies to achieve the opposite; they choose their disclosure policies to increase both the competitor's and their own supply.

¹⁴See appendix for the details.

¹⁵See appendix for details.