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Entropy and the value of information for investors

Author

Listed:
  • Antonio Cabrales

    () (Universidad Carlos III de Madrid)

  • Olivier Gossner

    () (Paris School of Economics and LSE)

  • Roberto Serrano

    () (Brown University and IMDEA Social Sciences Institute)

Abstract

Consider any investor who fears ruin facing any set of investments that satisfy no-arbitrage. Before investing, he can purchase information about the state of nature in the form of an information structure. Given his prior, information structure alpha is more informative than information structure beta if whenever he rejects alpha at some price, he also rejects beta at that price. We show that this complete informativeness ordering is represented by the decrease in entropy of his beliefs, regardless of his preferences, initial wealth or investment problem. It is also shown that no prior-independent informativeness ordering based on similar premises exists.

Suggested Citation

  • Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2010. "Entropy and the value of information for investors," Working Papers 2010-23, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  • Handle: RePEc:imd:wpaper:wp2010-23
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    References listed on IDEAS

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    1. Thierry Post & Martijn J. van den Assem & Guido Baltussen & Richard H. Thaler, 2008. "Deal or No Deal? Decision Making under Risk in a Large-Payoff Game Show," American Economic Review, American Economic Association, vol. 98(1), pages 38-71, March.
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    6. Azrieli, Yaron & Lehrer, Ehud, 2008. "The value of a stochastic information structure," Games and Economic Behavior, Elsevier, vol. 63(2), pages 679-693, July.
    7. Sergiu Hart, 2011. "Comparing Risks by Acceptance and Rejection," Journal of Political Economy, University of Chicago Press, vol. 119(4), pages 617-638.
    8. Susan Athey & Jonathan Levin, 1998. "The Value of Information In Monotone Decision Problems," Working papers 98-24, Massachusetts Institute of Technology (MIT), Department of Economics.
    9. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, September.
    10. Olivier Gossner & Tristan Tomala, 2006. "Empirical Distributions of Beliefs Under Imperfect Observation," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 13-30, February.
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    Cited by:

    1. Alexis Toda, 2015. "Bayesian general equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(2), pages 375-411, February.
    2. Antonio Jiménez-Martínez, 2015. "A model of belief influence in large social networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 21-59, May.
    3. Antony Millner & Daniel Heyen, 2017. "Valuing predictability," GRI Working Papers 260, Grantham Research Institute on Climate Change and the Environment.
    4. Luc Bridet & Margaret Leighton, 2015. "The Major Decision: Labor Market Implications of the Timing of Specialization in College," Discussion Paper Series, Department of Economics 201510, Department of Economics, University of St. Andrews.
    5. repec:eee:reecon:v:72:y:2018:i:1:p:101-116 is not listed on IDEAS
    6. Kyungmin Kim & Benjamin Lester & Braz Camargo, 2012. "Subsidizing Price Discovery," 2012 Meeting Papers 338, Society for Economic Dynamics.
    7. Cabrales, Antonio & Gossner, Olivier & Serrano, Roberto, 2017. "A normalized value for information purchases," Journal of Economic Theory, Elsevier, vol. 170(C), pages 266-288.
    8. repec:spr:annopr:v:262:y:2018:i:2:d:10.1007_s10479-016-2256-7 is not listed on IDEAS
    9. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.
    10. Stark, Oded & Jakubek, Marcin & Falniowski, Fryderyk, 2014. "Reconciling the Rawlsian and the utilitarian approaches to the maximization of social welfare," Economics Letters, Elsevier, vol. 122(3), pages 439-444.
    11. Bellalah, Mondher, 2016. "Shadow costs of incomplete information and short sales in the valuation of the firm and its assets," The North American Journal of Economics and Finance, Elsevier, vol. 37(C), pages 406-419.
    12. repec:eee:ecolet:v:164:y:2018:i:c:p:62-64 is not listed on IDEAS
    13. Agostino Manduchi, 2013. "Non-neutral information costs with match-value uncertainty," Journal of Economics, Springer, vol. 109(1), pages 1-25, May.
    14. repec:eee:gamebe:v:109:y:2018:i:c:p:21-39 is not listed on IDEAS
    15. Volha Audzei, 2015. "Information Acquisition and Excessive Risk: Impact of Policy Rate and Market Volatility," ACTA VSFS, University of Finance and Administration, vol. 9(2), pages 115-135.
    16. Braz Camargo, 2011. "Career Concerns: A Human Capital Perspective," 2011 Meeting Papers 1274, Society for Economic Dynamics.
    17. Mariana Cunha & António Osório & Ricardo Ribeiro, 2016. "Endogenous product design and quality with rationally inattentive consumers," Working Papers de Economia (Economics Working Papers) 03, Católica Porto Business School, Universidade Católica Portuguesa.
    18. 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.
    19. Li, Jian & Zhou, Junjie, 2016. "Blackwell's informativeness ranking with uncertainty-averse preferences," Games and Economic Behavior, Elsevier, vol. 96(C), pages 18-29.
    20. Lindbeck, Assar & Weibull, Jörgen, 2017. "Investment, Rational Inattention, and Delegation," Working Paper Series 1171, Research Institute of Industrial Economics.

    More about this item

    Keywords

    informativeness; information structures; entropy; decision under uncertainty; investment; Blackwell ordering;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D00 - Microeconomics - - General - - - General
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G00 - Financial Economics - - General - - - General
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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