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The Pandora's Box Problem with Sequential Inspections

Author

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  • Ali Aouad
  • Jingwei Ji
  • Yaron Shaposhnik

Abstract

The Pandora's box problem (Weitzman 1979) is a core model in economic theory that captures an agent's (Pandora's) search for the best alternative (box). We study an important generalization of the problem where the agent can either fully open boxes for a certain fee to reveal their exact values or partially open them at a reduced cost. This introduces a new tradeoff between information acquisition and cost efficiency. We establish a hardness result and employ an array of techniques in stochastic optimization to provide a comprehensive analysis of this model. This includes (1) the identification of structural properties of the optimal policy that provide insights about optimal decisions; (2) the derivation of problem relaxations and provably near-optimal solutions; (3) the characterization of the optimal policy in special yet non-trivial cases; and (4) an extensive numerical study that compares the performance of various policies, and which provides additional insights about the optimal policy. Throughout, we show that intuitive threshold-based policies that extend the Pandora's box optimal solution can effectively guide search decisions.

Suggested Citation

  • Ali Aouad & Jingwei Ji & Yaron Shaposhnik, 2025. "The Pandora's Box Problem with Sequential Inspections," Papers 2507.07508, arXiv.org.
  • Handle: RePEc:arx:papers:2507.07508
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    References listed on IDEAS

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    1. Michael Choi & Anovia Yifan Dai & Kyungmin Kim, 2018. "Consumer Search and Price Competition," Econometrica, Econometric Society, vol. 86(4), pages 1257-1281, July.
    2. Weitzman, Martin L, 1979. "Optimal Search for the Best Alternative," Econometrica, Econometric Society, vol. 47(3), pages 641-654, May.
    3. Leon Yang Chu & Hamid Nazerzadeh & Heng Zhang, 2020. "Position Ranking and Auctions for Online Marketplaces," Management Science, INFORMS, vol. 66(8), pages 3617-3634, August.
    4. Raluca M. Ursu, 2018. "The Power of Rankings: Quantifying the Effect of Rankings on Online Consumer Search and Purchase Decisions," Marketing Science, INFORMS, vol. 37(4), pages 530-552, August.
    5. Peter Gibbard, 2022. "A Model of Search with Two Stages of Information Acquisition and Additive Learning," Management Science, INFORMS, vol. 68(2), pages 1212-1217, February.
    6. David B. Brown & James E. Smith, 2013. "Optimal Sequential Exploration: Bandits, Clairvoyants, and Wildcats," Operations Research, INFORMS, vol. 61(3), pages 644-665, June.
    7. Xavier Gabaix & David Laibson & Guillermo Moloche & Stephen Weinberg, 2006. "Costly Information Acquisition: Experimental Analysis of a Boundedly Rational Model," American Economic Review, American Economic Association, vol. 96(4), pages 1043-1068, September.
    8. Olszewski, Wojciech & Weber, Richard, 2015. "A more general Pandora rule?," Journal of Economic Theory, Elsevier, vol. 160(C), pages 429-437.
    9. Doval, Laura, 2018. "Whether or not to open Pandora's box," Journal of Economic Theory, Elsevier, vol. 175(C), pages 127-158.
    10. Vishwanath, Tara, 1992. "Parallel Search for the Best Alternative," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(4), pages 495-507, October.
    11. Miller, Robert A, 1984. "Job Matching and Occupational Choice," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 1086-1120, December.
    12. Babur De Los Santos & Ali Hortacsu & Matthijs R. Wildenbeest, 2012. "Testing Models of Consumer Search Using Data on Web Browsing and Purchasing Behavior," American Economic Review, American Economic Association, vol. 102(6), pages 2955-2980, October.
    13. Santiago R. Balseiro & David B. Brown, 2019. "Approximations to Stochastic Dynamic Programs via Information Relaxation Duality," Operations Research, INFORMS, vol. 67(2), pages 577-597, March.
    14. Jake Clarkson & Kevin D. Glazebrook & Kyle Y. Lin, 2020. "Fast or Slow: Search in Discrete Locations with Two Search Modes," Operations Research, INFORMS, vol. 68(2), pages 552-571, March.
    15. Robert, Jacques & Stahl, Dale O, II, 1993. "Informative Price Advertising in a Sequential Search Model," Econometrica, Econometric Society, vol. 61(3), pages 657-686, May.
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