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Relatively robust decisions

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  • Thomas A. Weber

    (Chair of Operations, Economics and Strategy, École Polytechnique Fédérale de Lausanne)

Abstract

It is natural for humans to judge the outcome of a decision under uncertainty as a percentage of an ex-post optimal performance. We propose a robust decision-making framework based on a relative performance index. It is shown that if the decision maker’s preferences satisfy quasisupermodularity, single-crossing, and a nondecreasing log-differences property, the worst-case relative performance index can be represented as the lower envelope of two extremal performance ratios. The latter is used to characterize the agent’s optimal robust decision, which has implications both computationally and for obtaining closed-form solutions. We illustrate our results in an application which compares the performance of relative robustness to solutions that optimize worst-case payoffs, maximum absolute regret, and expected payoffs under a Laplacian prior.

Suggested Citation

  • Thomas A. Weber, 2023. "Relatively robust decisions," Theory and Decision, Springer, vol. 94(1), pages 35-62, January.
  • Handle: RePEc:kap:theord:v:94:y:2023:i:1:d:10.1007_s11238-022-09866-z
    DOI: 10.1007/s11238-022-09866-z
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    References listed on IDEAS

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    1. David E. Bell, 1982. "Regret in Decision Making under Uncertainty," Operations Research, INFORMS, vol. 30(5), pages 961-981, October.
    2. Retsef Levi & Georgia Perakis & Joline Uichanco, 2015. "The Data-Driven Newsvendor Problem: New Bounds and Insights," Operations Research, INFORMS, vol. 63(6), pages 1294-1306, December.
    3. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    4. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    5. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
    6. René Caldentey & Ying Liu & Ilan Lobel, 2017. "Intertemporal Pricing Under Minimax Regret," Operations Research, INFORMS, vol. 65(1), pages 104-129, February.
    7. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    8. Dirk Bergemann & Karl H. Schlag, 2012. "Pricing Without Priors," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 12, pages 405-415, World Scientific Publishing Co. Pte. Ltd..
    9. Jon M. Conrad, 1980. "Quasi-Option Value and the Expected Value of Information," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 94(4), pages 813-820.
    10. Ashish Goel & Adam Meyerson & Thomas Weber, 2009. "Fair welfare maximization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(3), pages 465-494, December.
    11. Robert B. Wilson, 2021. "Strategic Analysis of Auctions," Econometrica, Econometric Society, vol. 89(2), pages 555-561, March.
    12. Andrew E. B. Lim & J. George Shanthikumar & Gah-Yi Vahn, 2012. "Robust Portfolio Choice with Learning in the Framework of Regret: Single-Period Case," Management Science, INFORMS, vol. 58(9), pages 1732-1746, September.
    13. Milgrom, Paul & Roberts, John, 1990. "The Economics of Modern Manufacturing: Technology, Strategy, and Organization," American Economic Review, American Economic Association, vol. 80(3), pages 511-528, June.
    14. Arun Sundararajan, 2004. "Nonlinear Pricing of Information Goods," Management Science, INFORMS, vol. 50(12), pages 1660-1673, December.
    15. Buket Avci & Karan Girotra & Serguei Netessine, 2015. "Electric Vehicles with a Battery Switching Station: Adoption and Environmental Impact," Management Science, INFORMS, vol. 61(4), pages 772-794, April.
    16. René Caldentey & Ying Liu & Ilan Lobel, 2017. "Intertemporal Pricing Under Minimax Regret," Operations Research, INFORMS, vol. 65(1), pages 104-129, February.
    17. H E Mausser & M Laguna, 1999. "Minimising the maximum relative regret for linear programmes with interval objective function coefficients," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(10), pages 1063-1070, October.
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