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Pricing without Priors

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Abstract

We consider the problem of pricing a single object when the seller has only minimal information about the true valuation of the buyer. Specifically, the seller only knows the support of the possible valuations and has no further distributional information. The seller is solving this choice problem under uncertainty by minimizing her regret. The pricing policy hedges against uncertainty by randomizing over a range of prices. The support of the pricing policy is bounded away from zero. Buyers with low valuations cannot generate substantial regret and are priced out of the market. We generalize the pricing policy without priors to encompass many buyers and many qualities.

Suggested Citation

  • Dirk Bergemann & Karl H. Schlag, 2007. "Pricing without Priors," Cowles Foundation Discussion Papers 1625, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1625
    Note: CFP 1224.
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    References listed on IDEAS

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    1. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    2. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    3. 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..
    4. Neeman, Zvika, 2003. "The effectiveness of English auctions," Games and Economic Behavior, Elsevier, vol. 43(2), pages 214-238, May.
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    Cited by:

    1. Stoye, Jörg, 2011. "Axioms for minimax regret choice correspondences," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2226-2251.
    2. Dirk Bergemann & Stephen Morris, 2011. "Robust Mechanism Design: An Introduction," Cowles Foundation Discussion Papers 1818, Cowles Foundation for Research in Economics, Yale University.
    3. Król, Michał, 2012. "Product differentiation decisions under ambiguous consumer demand and pessimistic expectations," International Journal of Industrial Organization, Elsevier, vol. 30(6), pages 593-604.
    4. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    5. Ng, Tsan Sheng, 2013. "Robust regret for uncertain linear programs with application to co-production models," European Journal of Operational Research, Elsevier, vol. 227(3), pages 483-493.
    6. Stoye, Jörg, 2012. "Minimax regret treatment choice with covariates or with limited validity of experiments," Journal of Econometrics, Elsevier, vol. 166(1), pages 138-156.
    7. Montizaan, Raymond & Cörvers, Frank & de Grip, Andries & Dohmen, Thomas, 2012. "Negative Reciprocity and Retrenched Pension Rights," IZA Discussion Papers 6955, Institute for the Study of Labor (IZA).
    8. Krähmer, Daniel, 2012. "Auction design with endogenously correlated buyer types," Journal of Economic Theory, Elsevier, vol. 147(1), pages 118-141.
    9. Alexei Parakhonyak & Anton Sobolev, 2015. "Non‐Reservation Price Equilibrium and Search without Priors," Economic Journal, Royal Economic Society, vol. 0(584), pages 887-909, May.
    10. 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..
    11. Dirk Bergemann & Benjamin Brooks & Stephen Morris, 2016. "Informationally Robust Optimal Auction Design," Working Papers 084_2016, Princeton University, Department of Economics, Econometric Research Program..
    12. Vinicius Carrasco & Vitor Farinha Luz & Paulo Monteiro & Humberto Moreira, 2015. "Robust Selling Mechanisms," Textos para discussão 641, Department of Economics PUC-Rio (Brazil).
    13. Martin Szydlowski, 2012. "Ambiguity in Dynamic Contracts," Discussion Papers 1543, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    14. Handel, Benjamin R. & Misra, Kanishka & Roberts, James W., 2013. "Robust firm pricing with panel data," Journal of Econometrics, Elsevier, vol. 174(2), pages 165-185.
    15. Giordani, Paolo E. & Schlag, Karl H. & Zwart, Sanne, 2010. "Decision makers facing uncertainty: Theory versus evidence," Journal of Economic Psychology, Elsevier, vol. 31(4), pages 659-675, August.
    16. Garrett, Daniel F., 2014. "Robustness of simple menus of contracts in cost-based procurement," Games and Economic Behavior, Elsevier, vol. 87(C), pages 631-641.
    17. Čopič, Jernej & Ponsatí, Clara, 2016. "Optimal robust bilateral trade: Risk neutrality," Journal of Economic Theory, Elsevier, vol. 163(C), pages 276-287.
    18. Vinicius Carrasco & Vitor Farinha Luz & Paulo Monteiro & Humberto Moreira, 2015. "Robust Mechanisms: the curvature case," Textos para discussão 642, Department of Economics PUC-Rio (Brazil).
    19. Trivikram Dokka Venkata Satyanaraya & Sonali Sen Gupta & Fabrice Talla Nobibon & Alain Zemkoho, 2017. "Robust Toll Pricing," Working Papers 194217799, Lancaster University Management School, Economics Department.

    More about this item

    Keywords

    Monopoly; Optimal pricing; Regret; Multiple priors; Distribution free;

    JEL classification:

    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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