When are signals complements or substitutes? - Tilman Börgers; Angel Hernando-Veciana; Daniel Kröhmer (Northwestern University, Kellogg School of Management, Center for Mathematical Studies in Economics and Management Science, 2010)
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.
Keywords: C00; C44; D81; D83; 330; Complementarity; substitutability; value of information; Blackwell ordering