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A normalized value for information purchases

Antonio Cabrales (), Olivier Gossner and Roberto Serrano

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: Consider agents who are heterogeneous in their preferences and wealth levels. These agents may acquire information prior to choosing an investment that has a property of no-arbitrage, and each piece of information bears a corresponding cost. We associate a numeric index to each information purchase (information-cost pair). This index describes the normalized value of the information purchase: it is the risk-aversion level of the unique CARA agent who is indifferent between accepting and rejecting the purchase, and it is characterized by a \duality" principle that states that agents with a stronger preference for information should engage more often in information purchases. No agent more risk-averse than the index finds it profitable to acquire the information, whereas all agents less risk-averse than the index do. Given an empirically measured range of degrees of risk aversion in a competitive economy with no-arbitrage investments, our model therefore comes close to describ-ing an inverse demand for information, by predicting what pieces of information are acquired by agents and which ones are not. Among several desirable properties, the normalized-value formula induces a complete ranking of information structures that extends Blackwell's classic ordering.

Keywords: informativeness; information purchases; free energy; Kullback-Leibler divergence; relative entropy; decision under uncertainty; no-arbitrage investment; Blackwell ordering (search for similar items in EconPapers)
JEL-codes: L81 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-mic and nep-upt
Date: 2017-05-19
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Published in Journal of Economic Theory, 19, May, 2017, 170, pp. 266-288. ISSN: 0022-0531

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