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A normalized value for information purchases

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  • Cabrales, Antonio
  • Gossner, Olivier
  • Serrano, Roberto

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.

Suggested Citation

  • Cabrales, Antonio & Gossner, Olivier & Serrano, Roberto, 2017. "A normalized value for information purchases," LSE Research Online Documents on Economics 82501, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:82501
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    Cited by:

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    2. Michel de Lara & Olivier Gossner, 2020. "Payoffs-Beliefs Duality and the Value of Information," Post-Print hal-01941006, HAL.
    3. Luciano Pomatto & Philipp Strack & Omer Tamuz, 2018. "The Cost of Information: The Case of Constant Marginal Costs," Papers 1812.04211, arXiv.org, revised Feb 2023.
    4. Andrew Kosenko, 2021. "Algebraic Properties of Blackwell's Order and A Cardinal Measure of Informativeness," Papers 2110.11399, arXiv.org.
    5. Corgnet, Brice & Deck, Cary & DeSantis, Mark & Porter, David, 2018. "Information (non)aggregation in markets with costly signal acquisition," Journal of Economic Behavior & Organization, Elsevier, vol. 154(C), pages 286-320.
    6. Michel De Lara & Olivier Gossner, 2017. "An instrumental approach to the value of information," Working Papers 2017-49, Center for Research in Economics and Statistics.
    7. Jaehyuk Choi & Lan Ju & Jian Li & Zhiyong Tu, 2023. "Information extraction and artwork pricing," Papers 2302.08167, arXiv.org.

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    More about this item

    Keywords

    informativeness; information purchases; free energy; Kullback-Leibler divergence; relative entropy; decision under uncertainty; no-arbitrage investment; Blackwell ordering;
    All these keywords.

    JEL classification:

    • L81 - Industrial Organization - - Industry Studies: Services - - - Retail and Wholesale Trade; e-Commerce

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