When are signals complements or substitutes?

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 complementarity 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 characterization that permits an intuitive interpretation of complementarity and substitutability. We demonstrate how these conditions extend to more general settings. We also illustrate the implications of our concepts for three economic applications: information disclosure in auctions, information aggregation through voting, and polarization of beliefs.

[1]  N. Persico.  Information acquisition in auctions , 2000 .

[2]  E. Lehmann.  Comparing Location Experiments , 1988 .

[3]  James Andreoni,et al.  Diverging Opinions , 2007 .

[4]  Howard Raiffa,et al.  Games And Decisions , 1958 .

[5]  J. Dalmau.  “The more we know” , 2015, Neurology: Neuroimmunology & Neuroinflammation.

[6]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[7]  Joel Sobel,et al.  Information Aggregation and Grojp Decisions , 2006 .

[8]  L. Ross,et al.  Biased Assimilation and Attitude Polarization: The Effects of Prior Theories on Subsequently Considered Evidence , 1979 .

[9]  P. Kondor.  The more we know, the less we agree: public announcements and higher-order expectations , 2005 .

[10]  Gary B. Gorton,et al.  Trading, Communication and the Response of Asset Prices to News , 1993 .

[11]  N. Persico.  Committee Design with Endogenous Information , 2004 .

[12]  Patrick W. Schmitz,et al.  The (sub-)optimality of the majority rule , 2012, Games Econ. Behav..

[13]  M. Sarvary,et al.  Marketing Information: A Competitive Analysis , 1997 .

[14]  Paul Milgrom,et al.  Putting Auction Theory to Work , 2004 .

[15]  M. Rothschild,et al.  Increasing risk: I. A definition , 1970 .

[16]  Paul R. Milgrom,et al.  The value of information in a sealed-bid auction , 1982 .

[17]  M. A. Girshick,et al.  Theory of games and statistical decisions , 1955 .

[18]  T. Feddersen,et al.  Voting Behavior and Information Aggregation in Elections with Private Information , 1997 .

[19]  D. Blackwell.  Comparison of Experiments , 1951 .

[20]  Paul R. Milgrom,et al.  A theory of auctions and competitive bidding , 1982 .

[21]  A. McLennan.  Consequences of the Condorcet Jury Theorem for Beneficial Information Aggregation by Rational Agents , 1998, American Political Science Review.

[22]  Paul R. Milgrom,et al.  Rational Expectations, Information Acquisition, and Competitive Bidding , 1981 .

[23]  Susan Athey,et al.  The Value of Information in Monotone Decision Problems , 1998 .

[24]  Steven M. Medlin.  The value of information in a sealed bidding experiment , 1979 .

[25]  Andrea Prat,et al.  The Value of Public Information in Monopoly , 2001 .

[26]  D. Austen-Smith.  Information transmission in debate , 1990 .

[27]  Dean LeBaron,et al.  Trading , 1981 .

[28]  Yaron Azrieli,et al.  Pareto Efficiency and Weighted Majority Rules , 2014 .

[29]  Efe A. Ok.  Real analysis with economic applications , 2007 .