Research ArticleOpen AccessGoogle Scholar indexed
Multiplicative Normal Noise and Nonconcavity in the Value of Information
Sciences Po, Department of Economics, 28 rue des Saints Pères, Paris, France
- 1 Sciences Po, Department of Economics, 28 rue des Saints Pères, Paris, France
Theoretical Economics Letters·Volume 11 (2021)·Pages 116–124·Published 6 January 2021·DOI10.4236/tel.2021.111009
Copy link · social · email
Abstract
This paper investigates a Bayesian inverse problem of a price setting monopolist facing a random demand. In contrast to previous investigations an unknown true market potential of demand is distorted by two independent Gaussian errors, a zero-mean additive and a unity-mean multiplicative one. The multi-period game allows for learning from realized market demands (signals). Interestingly increasing the level of noise of a multiplicative error in this dynamic setting can actually improve the Value of Information of signals to the firm, a result that cannot hold for a single additive error or in a static context .
KeywordsValue of InformationInverse ProblemsBayesian LearningMonopolyMultiplicative NoiseNonconcavity
- Behringer, S. (2021). Expanding Multi-Market Monopoly and Nonconcavity in the Value of Information. http://www.stefanbehringer.com
- Chade, H., & Schlee, E. E. (2002). Another Look at the Radner-Stiglitz Nonconcavity in the Value of Information. Journal of Economic Theory, 107, 421-452. https://doi.org/10.1006/jeth.2001.2960
- De Lara, M., & Gilotte, L. (2007). A Tight Sufficient Condition for Radner-Stiglitz Nonconcavity in the Value of Information. Journal of Economic Theory, 137, 696-708. https://doi.org/10.1016/j.jet.2007.01.014
- Dunlop, M. M. (2019). Multiplicative Noise in Bayesian Inverse Problems: Well-Posedness and Consistency of MAP Estimators. arXiv Preprint. https://arxiv.org/abs/1910.14632
- Holmquist, B. (1988). Moments and Cumulants of the Multivariate Normal Distribution. Stochastic Analysis and Applications, 6, 273-278. https://doi.org/10.1080/07362998808809148
- Mirman, L. J., Samuelson, L., & Urbano, A. (1993). Monopoly Experimentation. International Economics Review, 34, 549-563. https://doi.org/10.2307/2527181
- Porter, R. (1983). Optimal Cartel Trigger Price Strategies. Journal of Economic Theory, 29, 313-338. https://doi.org/10.1016/0022-0531(83)90050-9
- Radner, R., & Stiglitz, J. (1984). A Nonconcavity in the Value of Information. In M. Boyer, & R. Kihlstrom (Eds), Bayesian Models of Economic Theory (pp. 33-52). Amsterdam: Elsevier.
- Saloner, G. (1984). Dynamic Equilibrium Limit-Pricing in An Uncertain Environment. MIT Department of Economics Working Paper Series, Report No. 342. http://hdl.handle.net/1721.1/63444
- Slade, M. (1989). Price Wars in Price-Setting Supergames. Economica, 56, 295-310. https://doi.org/10.2307/2554279
- Stratonovich, R. L. (1970). Detection and Estimation of Signals in Noise when One or Both Are Non-Gaussian. Proceedings of the IEEE, 58, 670-679. https://doi.org/10.1109/PROC.1970.7722
- Veldkamp, L. (2011). Information Economics in Macroeconomics and Finance. Princeton, NJ: Princeton University Press. https://doi.org/10.2307/j.ctvcm4j91
- Vives, X. (2010). Information and Learning in Markets: The Impact of Market Microstructure. Princeton, NJ: Princeton University Press. https://doi.org/10.2307/j.ctt7tc3b
- Weber, T. A., (2019). Dynamic Learning in Markets: Pricing, Advertising, and Information Acquisition. Proceedings of the 52nd Annual Hawaii International Conference on System Sciences (HICSS). Honolulu, 8-11 January 2019, 6628-6637. https://doi.org/10.24251/HICSS.2019.794