When are Signals Complements or Substitutes?

Börgers, Tilman and Hernando-Veciana, Angel and Krähmer, Daniel (2010): When are Signals Complements or Substitutes?

Abstract

The paper introduces a notion of complementarity (substitutability) of two signals which requires that in all decision problems each signal becomes more (less) valuable when the other signal becomes available. We provide a general characterization which relates com- plementarity and substitutability to a Blackwell comparison of two auxiliary signals. In a setting with a binary state space and binary signals, we find an explicit characteriza- tion that permits an intuitive interpretation of complementarity and substitutability. We demonstrate how these conditions extend to more general settings.

• Item Type: MPRA Paper
• Language: English
• Keywords: Information, signals, complementarity, substitutability.
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D80 - General

References

Susan Athey and Jonathan Levin (2001), "The Value of Information in Monotone Decision Problems," mimeo., Stanford.

Ken Binmore (2009), "Rational Decisions," Princeton: Princeton University Press.

David Blackwell (1951), "Comparison of Experiments," in: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley and Los Angeles: University of California Press, 93-102.

David Blackwell and M. A. Girshick (1954), "Theory of Games And Statistical Decisions," New York: John Wiley and Sons.

James Dow and Gary Gorton (1993), "Trading, Communication and the Response of Asset Prices to News," Economic Journal 103, 639-646.

Ian Jewitt (2007), "Information Order in Decisions and Agency Problems," mimeo., Nuffield College, Oxford.

Erich L. Lehmann (1988), "Comparing Location Experiments," Annals of Statistics 16, 521-533.

R. Duncan Luce and Howard Raiffa (1957), Games and Decisions, New York: John Wiley and Sons.

Paul Milgrom and Robert J. Weber (1982), "The Value of Information in a Sealed-Bid Auction," Journal of Mathematical Economics 10, 105-114.

Efe Ok (2007), Real Analysis With Economic Applications, Princeton: Princeton University Press.

Nicola Persico (2000), "Information Acquisition in Auctions," Econometrica 68, 135-48.

Nicola Persico (2004), "Committee Design with Endogenous Information," Review of Economic Studies 71, 165-191.

Roy Radner and Joseph Stiglitz (1984), "A Nonconcavity in the Value of Information," in: Boyer, M., and R. E. Kihlstrom (eds.), Bayesian Models in Economic Theory, Amsterdam and New York: North-Holland Publishing Company, 33-52.

Miklos Sarvary and Philip M. Parker (1997), "Marketing Information: A Competitive Analysis," Marketing Science 16, 24-38.

John von Neumann and Oskar Morgenstern (1953), Theory of Games and Economic Behavior (3rd edition), Princeton: Princeton University Press.