Abstract
There have been so many papers on the theory of oligopoly and information. In spite of growing literature on this subject, however, we believe that there is nevertheless a conspicuously missing link in it. To our surprise, very few papers have ever attempted to investigate an important subject of “information exchange and risk aversion.” Although such a subject seems to demand very tough computations and psychological pains, we strongly believe that someone must take up a challenge. So, the main purpose of this paper is to do our best for filling in such a missing gap, thus hoping to do a contribution to the important subject of oligopoly and information. More specifically, this paper aims to discuss the value of additional information in Cournot duopoly when each firm faces its own cost uncertainty. If firms display risk aversion and thus maximize the expected utility of profits, the exchange of cost information between them affects the mean values of outputs as well as their variances. By employing a constant absolute risk aversion model, we are able to show the variance effect may sometimes overpower the mean effect, whence information sharing may possibly make firms worse off. As our daily experience shows, “going together” may sometimes be a better policy than “going alone.”
This chapter is a completely revised version of Sakai-Yoshizumi (1991a). Sakai has exerted all his energy for revitalizing it in line with more recent developments of oligopoly theory under imperfect information. We wish to dedicate this article to the fond memory of our old friend Mr. Akihito Yoshizumi, who unfortunately retired from active academic work some time ago.
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Notes
- 1.
The year of 1970, when Arrow’s Essays were first published, can be regarded as a very “memorial year” in the sense that it well represents the dawn of a new era named “Risk and Uncertainty.” Together with Akerlof, Spence, and Stiglitz, the Great Figure Arrow was a good representative of the “A-S Age,” which was so-called by collecting “A” and “S,” the initials of those four pioneers. Arrow’s Essays have been given Sakai a great shock until today. Personally speaking, we are so happy to say that both Sakai and Sasaki have the lucky initial “S.” For details, see Sakai (1982).
- 2.
Bernoulli (1738) was first published in Latin as a mathematical paper at St. Petersburg, the capital of the Russian Empire, and more than two hundred years later translated in English. In this epoch-making and long standing paper, he boldly introduced the Law of Decreasing Marginal Utilities, which was an outstanding achievement in the history of economic thought, being far ahead of the times of the Marginal Revolution in the 1980s. This clearly tells as that Bernoulli was also historically first scholar who introduced the concept of Risk Aversion in the Theory of Decision Making under Risk.
- 3.
For those long years from the 1970s to the present, there have been a vast volume of papers on oligopoly and information. See Basar and Ho (1974), Ponssard (1979a, 1979b), Clark (1985), Vives (1984, 1999, 2002, 2008), Okada (1984), Sakai (1985, 1990, 1991, 1993, 2015), Sakai and Yoshizumi (1991a, 1991b), Shapiro (1986), Gal-Or (1985), Demange and Laroque (1995), Raith (1996), Jin (1998), and many others.
- 4.
For the properties of the conditional probability of the multivariate normal distribution, see Mood and Graybill (1963). More generally, let the two-dimensional random variable (x, y) have the bivariate normal distribution with mean (μx, μy) and variance (σx 2, σy 2). Then the conditional density of y, given x, is normal with mean μx + (ρσy /σx) (x −μx) and variance σy 2 (1 −ρ2).
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Sakai, Y., Sasaki, K. (2021). Information Sharing of Private Cost Information: An Application of the Cardano Cubic Formula. 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_9
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