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Editor: Universidad Carlos III de Madrid. Departamento de Economía

Issued date: 2007-03

ISSN: 2340-5031

Serie-No.: UC3M Working papers. Economics07-15

Keywords: Complementarity , Substitutability , Value of information , Blackwell-ordering , Statistical decision problem , Information acquisition , Second price auction

Rights: Atribución-NoComercial-SinDerivadas 3.0 España

Abstract:The paper introduces a notion of complementarity (substitutability) of two signals whichrequires that in all decision problems each signal becomes more (less) valuable when theother signal becomes available. We provide a general characterization which relaThe paper introduces a notion of complementarity (substitutability) of two signals whichrequires that in all decision problems each signal becomes more (less) valuable when theother signal becomes available. We provide a general characterization which relatescomplementarity and substitutability to a Blackwell-comparison of two auxiliary signals. Ina special setting with a binary state space and binary, symmetric signals, we find an explicitcharacterization that permits an intuitive interpretation of complementarity andsubstitutability. We demonstrate how these conditions extend to the general case. Finally,we study implications of complementarity and substitutability for information acquisitionand in a second price auction.+-





Author: Börgers, Tilman; Hernando-Veciana, Ángel; Krähmer, Daniel

Source: http://e-archivo.uc3m.es


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Universidad Carlos III de Madrid Repositorio institucional e-Archivo http:--e-archivo.uc3m.es Departamento de Economía DE - Working Papers.
Economics.
WE 2007-03 When are signals complements or substitutes? Börgers, Tilman http:--hdl.handle.net-10016-679 Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid Working Paper 07-25 Economic Series 15 March 2007 Departamento de Economía Universidad Carlos III de Madrid Calle Madrid, 126 28903 Getafe (Spain) Fax (34-91) 6249875 WHEN ARE SIGNALS COMPLEMENTS OR SUBSTITUTES?∗ Tilman Börgers†, Angel Hernando-Veciana‡, and Daniel Krähmer§ 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 complementarity and substitutability to a Blackwell-comparison of two auxiliary signals.
In a special setting with a binary state space and binary, symmetric signals, we find an explicit characterization that permits an intuitive interpretation of complementarity and substitutability.
We demonstrate how these conditions extend to the general case.
Finally, we study implications of complementarity and substitutability for information acquisition and in a second price auction. Keywords: Complementarity, substitutability, value of information, Blackwell- ordering, statistical decision problem, information acquisition, second price auction JEL Classification: C00, C44, D81, D83 ∗ Angel Hernando-Veciana acknowledges financial support by the Spanish Ministerio de Ciencia y Tecnologia through project SEJ2006-11665-C02-02.
Daniel Krähmer acknowledges financial support by the German Science Foundation (DFG) through SFB-TR 15. † Department of Economics, University of Michigan, tborgers@umich.edu. ‡ Departament of Economics Universidad Carlos III de Madrid, angel.hernando@...





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