Welfare Effects of Endogenous Information Acquisition and Disclosure in Duopoly Markets

Abstract

This paper investigates the interaction between firms' information acquisition decisions and disclosure of internally acquired information in a Cournot duopoly market under demand uncertainty. The main results are as follows. When the correlation between firms' demands is positive and sufficiently high, disclosure of information on demand uncertainty can enhance social welfare, given that the quality of firms' private information is constant. However, in the setting where firms' private information is endogenously determined, mandatory disclosure is not always desirable. This is because, when disclosure is mandated, firms acquire less precise information compared with the case where the acquired information is not disclosed; hence, their internal information environments are deteriorated. This can lead to unintended consequences such that disclosure regulation decreases social welfare.

Keywords:

• Information acquisition
• Disclosure
• Duopoly
• Social welfare

Acknowledgments

For their constructive comments and suggestions I would like to thank Robert Göx (associate editor) and two anonymous reviewers. This paper is based on a chapter of my dissertation at Osaka University. I am grateful to my committee members: Atsushi Shiiba (chair), Tatsushi Yamamoto, and Katsuhiko Muramiya. I would also like to thank Masahiro Enomoto, Ken-Ichi Shimomura, Satoshi Taguchi, Hiroji Takao, Masayuki Ueeda, Hidetoshi Yamaji, and seminar participants at Osaka University, Kobe University, Doshisha University, and Aoyama Gakuin University for helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Supplemental Data and Research Materials

Supplemental data for this article can be accessed on the Taylor & Francis website, doi:10.1080/09638180.2019.1615969.

Notes

1 See, for example, Vives (1984, 1990), Gal-Or (1985), Kirby (1988), Darrough (1993), Sankar (1995), Raith (1996), Clinch and Verrecchia (1997), Pae (2000, 2002), Arya and Mittendorf (2007), Hughes and Williams (2008), Arya, Frimor, and Mittendorf (2010), Bagnoli and Watts (2010, 2015), Corona and Nan (2013), Suijs and Wielhouwer (2014), and Hughes and Pae (2015).

2 Ganuza and Jansen (2013) consider general information structures and use new information orderings based on the dispersion of conditional expectations. By contrast, based on the assumption of noisy normally distributed signals, this paper examines how the welfare effects of disclosure can change depending on the parameters if information precision is endogenous.

3 The basic structure and notations of the model are based on Darrough (1993), Arya and Mittendorf (2007), and Suijs and Wielhouwer (2014).

4 Most theoretical studies that analyze firms' disclosure decisions in duopoly/oligopoly markets consider two types of uncertainty: demand uncertainty and cost uncertainty. In other words, firms have private information about market demand or their own production costs. In Cournot competition, however, the key distinction is between industry-wide versus firm-specific information, not between demand versus cost information (Christensen & Feltham, 2003, Chapter 15).

5 Notice that when $r\to 1$ ($r\to 0$), the firms face industry-wide (firm-specific) uncertainty. Although r does not equal the correlation between demand parameters in a strict sense, I simply refer to r as the correlation between them. See Suijs and Wielhouwer (2014, p.230, footnote 6).

6 Following previous studies, despite the normality assumption about $\mathrm{\Delta }{\alpha }_i$ and ${\epsilon }_i$, I ignore the possibility of negative quantities. See, for example, Vives (1984, p.77, footnote 2), Darrough (1993, p.541, footnote 15), and Suijs and Wielhouwer (2014, p.232. footnote 8).

7 This expression of the information acquisition cost is the same as that used by Hauk and Hurkens (2001).

8 This definition about the quality of the signal is consistent with that of Ganuza and Jansen (2013). The information criterion of Ganuza and Jansen (2013), called Integral Precision, is based on ‘the principle that an information structure …is more informative (more precise) than another if it generates more dispersed conditional expectations’(p.850).

9 Ganuza and Jansen (2013) also use this formulation for the disclosure policy of the firm for the same reason as I do. See, Ganuza and Jansen (2013, p.850, footnote 9). As we will see in the following sections, corner solutions (i.e., ${\theta }_i=0\mathrm{o}\mathrm{r}1$) arise according to the types of information and competition in voluntary disclosure settings. That is, in equilibrium, the signal acquired by each firm i is fully disclosed or completely concealed.

10 Note that if firm j's signal is not disclosed, information of the undisclosed signal quality is not useful for firm i.

11 See, for example, Penno (1996) and Subramanyam (1996).

12 Note that the information is only received after both choices are made.

13 Note that because both firms are assumed to commit themselves to the disclosure policy before they acquire and observe the signal, the choice of nondisclosure does not convey any information about the realization of the signal.

14 The derivation is presented in the online technical appendix.

15 Note that the second derivative of the objective function is $-2k/s(1-{\eta }_i{)}^3$; thus, the second-order condition is satisfied because ${\eta }_i\in [0,1)$.

16 As shown by Suijs and Wielhouwer (2014), this condition coincides with the condition under which nondisclosure arises in equilibrium.

17 This result is consistent with Suijs and Wielhouwer (2014, Proposition 1).

18 Specifically, $\overline{k}$ is given by $\overline{k}=\frac{3s^2(4-{\gamma }^2{)}^2(1-{\eta }_i{)}^2+s^2(2r-\gamma )\left[4\right(6r-5\gamma )+{\gamma }^2(3-2r\left)\right](1-{\eta }_i{)}^2{\theta }_i}{8(4-{\gamma }^2{)}^2}.$

19 See Figure 2 of Suijs and Wielhouwer (2014).

Additional information

Funding

This work was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers JP16K17206 and JP19K13851.