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The Relationship Between Perfect and Imperfect Information in a Two-Action Risk-Sensitive Problem

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  • J. Eric Bickel

    (Department of Industrial and Systems Engineering, Texas A&M University, College Station, Texas 77843)

Abstract

The ability to value information is a central feature of decision analysis and one of its most interesting areas of application. Unfortunately, general assertions regarding the drivers of information value or its properties have been difficult to formulate or have been disproved by counterexample. In this paper, we investigate the value of imperfect information relative to perfect information (RVOI). Within the context of a two-action decision problem with normal priors and exponential utility, we derive a closed-form solution for the value of information and demonstrate that the RVOI is maximal when the decision maker is indifferent between the two alternatives. In addition, we determine when the value of an information system providing a normally distributed signal with correlation coefficient (rho) is equal to (rho) × 100% or (rho) 2 × 100% of the value of perfect information. These results deepen our understanding of information value and enable practitioners to estimate the value of imperfect information in particular settings.

Suggested Citation

  • J. Eric Bickel, 2008. "The Relationship Between Perfect and Imperfect Information in a Two-Action Risk-Sensitive Problem," Decision Analysis, INFORMS, vol. 5(3), pages 116-128, September.
    • Handle: RePEc:inm:ordeca:v:5:y:2008:i:3:p:116-128
    DOI: 10.1287/deca.1080.0118
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    References listed on IDEAS

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    1. Ronald W. Hilton, 1981. "The Determinants of Information Value: Synthesizing Some General Results," Management Science, INFORMS, vol. 27(1), pages 57-64, January.
    2. L. P. Fatti & A. Mehrez & M. Pachter, 1987. "Bounds and properties of the expected value of sample information for a project‐selection problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(1), pages 141-150, February.
    3. Samson, D. & Wirth, A. & Rickard, J., 1989. "The value of information from multiple sources of uncertainty in decision analysis," European Journal of Operational Research, Elsevier, vol. 39(3), pages 254-260, April.
    4. Gould, John P., 1974. "Risk, stochastic preference, and the value of information," Journal of Economic Theory, Elsevier, vol. 8(1), pages 64-84, May.
    5. Ronald A. Howard, 1971. "Proximal Decision Analysis," Management Science, INFORMS, vol. 17(9), pages 507-541, May.
    6. Abraham Mehrez, 1985. "Technical Note—The Effect of Risk Aversion on the Expected Value of Perfect Information," Operations Research, INFORMS, vol. 33(2), pages 455-458, April.
    7. Craig W. Kirkwood, 2004. "Approximating Risk Aversion in Decision Analysis Applications," Decision Analysis, INFORMS, vol. 1(1), pages 51-67, March.
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    Citations

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    Cited by:

    1. Vilkkumaa, Eeva & Liesiö, Juuso & Salo, Ahti, 2014. "Optimal strategies for selecting project portfolios using uncertain value estimates," European Journal of Operational Research, Elsevier, vol. 233(3), pages 772-783.
    2. L. Robin Keller & Ali Abbas & J. Eric Bickel & Vicki M. Bier & David V. Budescu & John C. Butler & Enrico Diecidue & Robin L. Dillon-Merrill & Raimo P. Hämäläinen & Kenneth C. Lichtendahl & Jason R. W, 2012. "From the Editors ---Brainstorming, Multiplicative Utilities, Partial Information on Probabilities or Outcomes, and Regulatory Focus," Decision Analysis, INFORMS, vol. 9(4), pages 297-302, December.
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      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2008. "From the Editors..," Decision Analysis, INFORMS, vol. 5(4), pages 173-176, December.
      • L. Robin Keller & Manel Baucells & John C. Butler & Philippe Delquié & Jason R. W. Merrick & Gregory S. Parnell & Ahti Salo, 2009. "From the Editors ..," Decision Analysis, INFORMS, vol. 6(4), pages 199-201, December.
    4. Niyazi Onur Bakir, 2015. "Monotonicity of the Selling Price of Information with Risk Aversion in Two Action Decision Problems," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 7(2), pages 71-90, June.
    5. James E. Smith & Canan Ulu, 2017. "Risk Aversion, Information Acquisition, and Technology Adoption," Operations Research, INFORMS, vol. 65(4), pages 1011-1028, August.
    6. Kun Zan & J. Eric Bickel, 2013. "Components of Portfolio Value of Information," Decision Analysis, INFORMS, vol. 10(2), pages 171-185, June.
    7. Niyazi Onur Bakır & Georgia-Ann Klutke, 2014. "Buying price of event information in two-action decision problems," Environment Systems and Decisions, Springer, vol. 34(1), pages 38-48, March.
    8. L. Robin Keller, 2008. "From the Editor..," Decision Analysis, INFORMS, vol. 5(3), pages 113-115, September.
    9. Ali E. Abbas & N. Onur Bakır & Georgia-Ann Klutke & Zhengwei Sun, 2013. "Effects of Risk Aversion on the Value of Information in Two-Action Decision Problems," Decision Analysis, INFORMS, vol. 10(3), pages 257-275, September.
    10. Adam Fleischhacker & Pak-Wing Fok & Mokshay Madiman & Nan Wu, 2023. "A Closed-Form EVSI Expression for a Multinomial Data-Generating Process," Decision Analysis, INFORMS, vol. 20(1), pages 73-84, March.
    11. Philippe Delquié, 2008. "The Value of Information and Intensity of Preference," Decision Analysis, INFORMS, vol. 5(3), pages 129-139, September.
    12. Rakesh K. Sarin, 2013. "From the Editor —Optimal Betting, Reducing Unnecessary Mammography in Breast Cancer Diagnosis, Product Line Design, and Value of Information," Decision Analysis, INFORMS, vol. 10(3), pages 187-188, September.
    13. Rakesh K. Sarin & L. Robin Keller, 2013. "From the Editors: Probability Approximations, Anti-Terrorism Strategy, and Bull's-Eye Display for Performance Feedback," Decision Analysis, INFORMS, vol. 10(1), pages 1-5, March.
    14. Zou, Guang & Faber, Michael Havbro & González, Arturo & Banisoleiman, Kian, 2021. "Computing the value of information from periodic testing in holistic decision making under uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 206(C).
    15. Whitney J. Trainor-Guitton, 2014. "A geophysical perspective of value of information: examples of spatial decisions for groundwater sustainability," Environment Systems and Decisions, Springer, vol. 34(1), pages 124-133, March.
    16. Jafarizadeh, Babak, 2012. "Information acquisition as an American option," Energy Economics, Elsevier, vol. 34(3), pages 807-816.
    17. Debarun Bhattacharjya & Jo Eidsvik & Tapan Mukerji, 2013. "The Value of Information in Portfolio Problems with Dependent Projects," Decision Analysis, INFORMS, vol. 10(4), pages 341-351, December.
    18. Debarun Bhattacharjya & Léa A. Deleris, 2014. "The Value of Information in Some Variations of the Stopping Problem," Decision Analysis, INFORMS, vol. 11(3), pages 189-203, September.
    19. Zhengwei Sun & Ali E. Abbas, 2014. "On the sensitivity of the value of information to risk aversion in two-action decision problems," Environment Systems and Decisions, Springer, vol. 34(1), pages 24-37, March.
    20. L. Robin Keller, 2009. "From the Editor..," Decision Analysis, INFORMS, vol. 6(3), pages 121-123, September.
    21. Hans Olav Vogt Myklebust & Jo Eidsvik & Iver Bakken Sperstad & Debarun Bhattacharjya, 2020. "Value of Information Analysis for Complex Simulator Models: Application to Wind Farm Maintenance," Decision Analysis, INFORMS, vol. 17(2), pages 134-153, June.
    22. Peter I. Frazier & Warren B. Powell, 2010. "Paradoxes in Learning and the Marginal Value of Information," Decision Analysis, INFORMS, vol. 7(4), pages 378-403, December.
    23. Rakesh K. Sarin & L. Robin Keller, 2013. "From the Editors ---Group Decisions, Preference Elicitation, Experienced Utility, Survival Probabilities, and Portfolio Value of Information," Decision Analysis, INFORMS, vol. 10(2), pages 99-102, June.

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