Aggregation of Information in Large Cournot Markets

Abstract

AGGREGATION OF INFORMATION IN LARGE COURNOT MARKETS BY XAVIER VIVES1 Consider a homogeneous product market where firms have private information about an uncertain demand parameter and compete in quantities. We examine the convergence properties of Bayesian-Cournot equilibria as the economy is replicated and conclude that large Cournot (or almost competitive) markets do not aggregate information efficiently except possibly when the production technology exhibits constant returns to scale. Even in a competitive market there is a welfare loss with respect to the first best outcome due to incomplete information in general. Nevertheless a competitive market is efficient, taking as given the decentralized private information structure of the economy. Endogenous (and costly) information acquisition is examined and seen to imply that the market outcome always falls short of the first best level with decreasing returns to scale. The results are also shown to be robust to the addition of extra rounds of competition which allows firms to use the information revealed by past prices. Explicit closed form solutions yielding comparative static results are obtained for models characterized by quadratic payoffs and affine information structures.

One-leader and multiple-follower Stackelberg games with private information

“…Assuming the cost of entering a market, we could endogenize the number of followers. Third, it might be useful to consider the implications of analyzing the social surplus as in the study of Vives (1984Vives ( , 1988Vives ( , 2008Vives ( , 2011, which addresses the large Cournot model with strictly convex production costs. While our paper chose to emphasize strategic situations, these three points merit attention in future research.…”

“…In another branch of the literature, Vives (1984Vives ( , 1988Vives ( , 2008Vives ( , 2011 and Myatt and Wallace (2013) analyze large Cournot games.…”

Endogenous private information structures

“…In the case of principal-agent theory Kessler (1998) has shown that the agent may prefer to stay uninformed, thereby crucially changing the incentive compatibility and individual rationality constraints of the principal's problem. Cremer and Khalil (1992) show that the principal may offer contracts that induce the agent to stay uninformed and that those contracts will be very different from 1 Notable exceptions are Vives (1988), Li et al (1987), Hwang (1993Hwang ( , 1995, Hauk and Hurkens (2001), and Ponssard (1979) that consider information acquisition in oligopolies, Lee (1982), Milgrom (1981), Matthews (1984), and Persico (1997) who consider the incentives for information acquisition in auctions and Khalil (1992, 1994), Cremer et al (1998), and Kessler (1998) that consider principal-agent relationships where the agent is initially uninformed but can acquire information, before or after the principal has offered him a contract. Grossman and Stiglitz (1980) initiated research on the incentives to acquire costly information on the value of a stock in financial markets.…”

Secret information acquisition in Cournot markets

“…2 Information acquisition was studied in Cournot markets by Chang and Lee 1992, Daughety and Reinganum 1992, Hwang 1993, 1995, Li et al 1987, Ockenfels 1989and Vives 1988. Matthews 1984and Milgrom 1981 studied information gathering in auctions.…”

“…Since Vives 1988 andLi et al 1987 were mainly interested in the competitive market, viewed as the limit of nite Cournot markets, it is interesting to analyze whether in the limit when the number of rms goes to in nity this di erence disappears. It does.…”