Abstract
The long series of papers on the information exchanges among firms and their welfare implications contain three parts, namely Part I, Part II, and Part III. In the previous chapters, we already discussed Parts I and II. Part I was concerned with the basic dual relations between the Cournot and Bertrand models. Part II dealt with the world of risk and uncertainty, focusing on the Cournot duopoly model with a common demand risk as a starting point. It then explored other types of duopoly models with a common risk. The purpose of this chapter is to discuss more complicated problems such as private risks and oligopoly models. When there exist more than two firms in an industry, the problem of the information exchange among firms becomes more complicated yet more intriguing. It will be seen that as the number of “producers as insiders” rises, the possibility of “consumers as outsiders” gaining their welfare is likely to increase. This is certainly the result which may agree with common sense. Some policy implications of our analysis will also be investigated.
This chapter is a completely revised version of the last part of Sakai (1989).
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Notes
- 1.
In the long history of duopoly and oligopoly models, there have been three big names; namely, A.A. Cournot (1838), J. Bertrand(1884), and H. von Stackelberg (1934). They were all concerned with those models in the limited situation of no risks, in which information acquisition and transmission did not play a significant role at all. Nash (1951) succeeded to generalize the equilibrium concept of Cournot (1838) to the game theoretic framework of Von Neumann & Morgenstern (1944). Harsanyi (1967-68), Selten (1973), and Basar & Ho (1974) studied informational properties of the Nash solution of games. Keeping those previous results in mind, this paper aims to shed new light on the new problem of information exchanges among Cournot or Bertrand firms with demand/cost risks being present. It should be noted that only in the 1980s, the factors of demand/cost information were introduced into the Cournot and Bertrand models. Since then until today, so many papers in the area of oligopoly and information have been published. We believe that this paper constitutes a systematic summary for those papers, hopefully indicating possible directions for future research. For previous summary and related works, see Sakai (1985, 1986, 1987, 1989, 1990a, 1990b, 1991), Kühn & Vives (1994), Raith (1996), Jin (1998) and others. Also see Scherer (1981).
- 2.
As far as the Cournot model is concerned, whether the information in question is about demand or cost does not matter at all. The line of research with the Cournot duopoly under private risks was initiated by Okada (1982) and Sakai (1985) for a homogenous product case, and was extended by Vives (1984, 1985), Gal-Or (1986), Fried (1984), Sakai (1986), and others to deal with a wider range of product differentiation.
- 3.
All of those sixteen cases were comprehensively discussed by Sakai (1985) for the extreme case of perfect substitutes (viz., θ = 1). While Fried (1984) was a fine piece of work doing the welfare analysis of information sharing within a similar framework, he picked up only nine cases out of those sixteen, and unfortunately failed to consider the welfare impact on consumers and the whole society. It is also noted that in his pioneering work, Okada (1982) limited his attention to barely four cases.
- 4.
For a graphical presentation only, we make the assumption of no correlation here (namely, ρ = 0). It is noted, however, that the welfare analysis of this paper can cover the whole range of correlation from minus unity to plus unity (namely, —1 ≦ρ ≦1). Since Gal-Or (1986) assumes that goods are substitutes and that stochastic parameters are non-correlated (namely, θ> 0 and ρ = 0), her analysis corresponds very well to Panel (A) in Fig. 6.2.
- 5.
- 6.
It is noted that, only in the 1980s, there emerged a number of papers dealing with the Bertrand model with demand/cost risks. More specifically, the Bertrand model with private demand risks was first intensively studied by Sakai (1987). It is unfortunate, however, that the welfare analysis of information sharing was not complete in this earlier paper. It not only failed to investigate the welfare impact on consumers and the whole society, but also neglected the decomposition into variation and efficiency channels.
- 7.
- 8.
The Betrand duopoly under private cost risks was studied by Gal-Or (1986) for the special case where goods are substitutes and costs are not correlated (i.e.,θ> 0 andρ = 0). However, the welfare impact on consumers and the whole society was not discussed in her otherwise excellent work. A more complete welfare analysis which allows for complementary goods and also for positively or negatively correlated costs was independently and thoroughly carried out by Sakai & Yamato (1988).
- 9.
- 10.
Such a nice symmetric case was investigated by Friedman (1986) and others for oligopoly models in the absence of any risks.
- 11.
The problem of information sharing in the Cournot oligopoly has been much concern in the modern theory of oligopoly and industrial organization. Gal-Or (1985), Li (1985), and Shapiro (1986) studied the problem for a very simple case of homogeneous products (namely, θ= 1) whereas Sakai (1988) worked with a more general case of product differentiation (—1 ≦ θ≦ 1) . There exist another group of papers such as Ponssard (1979), Clarke (1983), and Nalebuff & Zeckhauser (1986) which limited attention on the presence of only one risk, still maintaining the assumption of homogeneous products ( i.e., θ = 1). It is noted that if all private risks are perfectly and positively correlated (namely, ρ = 1), then the case of private risks may boil down to the one of a common risk.
- 12.
For the detailed derivation of these formulas, see Sakai (1989).
- 13.
Such a distinction between “a few” and “many” may be compared with the famous result of Selten (1973) who claims that four are “few” and six are “many.” In fact, using his own cartel-making model, Selten has shown that if there are at least as many as six firms in an industry then there emerges the completely new situation: every firm intends to stay out of the cartel and act as an outsider rather than remaining an insider. It seems that for any kind of economic model, there should exist a dividing line between “a few” and “many.”
- 14.
Because any tongue-like area in Fig. 6.4 is not exactly a symmetric figure, the point Mn is near yet not equal to the minimum point of the curve HnMnKn (n = 10, 20, 50). As Eq. (19) above may show, this curve is not a parabola but takes a more complicate shape.
- 15.
When there are a sufficiently large number of firms, our oligopoly framework taken here is presumably close to the monopolistic competition situation of Chamberlin (1933). Vives (1989) attempted to study incentives to share information and welfare in such large market.
- 16.
For a detailed welfare analysis of the Bertrand oligopoly with private cost risks, see Sakai & Yamato (1990). Vives (1989) discussed a similar problem within the framework of monopolistic competition.
- 17.
- 18.
- 19.
- 20.
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Sakai, Y., Sasaki, K. (2021). Information Exchange among Firms and Their Welfare Implications (Part III): Private Risks and Oligopoly Models. In: Information and Distribution. New Frontiers in Regional Science: Asian Perspectives, vol 49. Springer, Singapore. https://doi.org/10.1007/978-981-10-0101-7_6
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