The social value of information and the competition motive: price versus quantity games
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The social value of information and the competition motive: price versus quantity games Camille Cornand1
· Rodolphe Dos Santos Ferreira2,3
Received: 1 September 2017 / Accepted: 11 February 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract We propose a unified framework bridging the gap between team and competition issues in price and quantity games, played by producers of either substitutes or complements, when information is imperfect and dispersed. We reconsider the social value of private and public information in this context and compare the outcomes of the two types of games in terms of equilibrium and social welfare. By parting with full cooperation, the competition motive fitted into the payoffs introduces a strategy distortion and, when information is dispersed, an informational distortion, both increasing with the intensity of competition. The former affects the response to the expected value of the fundamental, and the latter translates into an inefficiently low (high) weight on public information under strategic complementarity (substitutability). Contrary to the latter, which vanishes in the absence of the competition motive, the former is eliminated, under strategic complementarity and dispersed information, at some positive strength of the competition motive, decreasing with the information quality. This disparity creates a trade-off between the minimization of each distortion. As to the social value of public information, it is always positive, while that of private information may be negative, again under strategic complementarity, if competition is intense and the quality of private information relatively poor. Finally, it is more profitable to play under strategic substitutability, except possibly for an intermediate range of the intensity of competition if the quality of private information is again relatively poor. Keywords Beauty contest · Price and quantity competition · Strategic substitutability and complementarity · (Anti-)coordination · Public and private information
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Camille Cornand [email protected] Rodolphe Dos Santos Ferreira [email protected]
1
CNRS, GATE UMR 5824, Univ Lyon, 93, Chemin des Mouilles, 69130 Ecully, France
2
BETA, University of Strasbourg, 61 avenue de la Forêt Noire, 67085 Strasbourg Cedex, France
3
Católica Lisbon School of Business and Economics, Lisbon, Portugal
123
C. Cornand, R. Dos Santos Ferreira
JEL Classification D43 · D82 · L13
1 Introduction The payoffs of Keynes’ beauty contest, as modeled by Morris and Shin (2002), involve three motives (Cornand and Heinemann 2008): a fundamental motive, making agents strive to predict and fit some exogenous fundamental value, a coordination motive, giving them an incentive to match the conventional value to be set by the market, and a competition motive, making them better off when beating the market. Should information be perfect, the fundamental and the coordination motives would be compatible: all agents would simply coordinate on the fundamental value. As information becomes
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