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Robust Monopoly Pricing: The Case of Regret


  • Dirk Bergemann
  • Karl Schlag


We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. The robust version of the problem is distinct in two aspects: (i) the seller minimizes regret rather than maximizes revenue, and (ii) the seller only knows that the true distribution of the valuations is in a neighborhood of a given model distribution. We characterize the robust pricing policy as the solution to a minimax problem for small and large neighborhoods. In contrast to the classic monopoly policy which is a single deterministic price, the robust policy is always a random pricing policy, or equivalently, a multi-item menu policy. The responsiveness of the robust policy to an increase in risk is determined by the curvature of the static profit function.

Suggested Citation

  • Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing: The Case of Regret," Economics Working Papers ECO2005/10, European University Institute.
  • Handle: RePEc:eui:euiwps:eco2005/10

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    1. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 381-419, March.
    2. Markku Lanne & Helmut Lütkepohl, 2008. "Identifying Monetary Policy Shocks via Changes in Volatility," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(6), pages 1131-1149, September.
    3. Ravn, Morten O. & Schmitt-Grohe, Stephanie & Uribe, Martín & Uuskula, Lenno, 2010. "Deep habits and the dynamic effects of monetary policy shocks," Journal of the Japanese and International Economies, Elsevier, vol. 24(2), pages 236-258, June.
    4. Cogley, Timothy & Nason, James M, 1995. "Output Dynamics in Real-Business-Cycle Models," American Economic Review, American Economic Association, vol. 85(3), pages 492-511, June.
    5. Canova, Fabio & Sala, Luca, 2009. "Back to square one: Identification issues in DSGE models," Journal of Monetary Economics, Elsevier, vol. 56(4), pages 431-449, May.
    6. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148 Elsevier.
    7. Leeper, Eric M., 1991. "Equilibria under 'active' and 'passive' monetary and fiscal policies," Journal of Monetary Economics, Elsevier, vol. 27(1), pages 129-147, February.
    8. Andrew Mountford & Harald Uhlig, 2009. "What are the effects of fiscal policy shocks?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(6), pages 960-992.
    9. Canova, Fabio & Sala, Luca, 2006. "Back to square one: identification issues in DSGE models," Working Paper Series 583, European Central Bank.
    10. Morten O. Ravn & Karel Mertens, 2008. "The Aggregate Effects of Anticipated and Unanticipated U.S. Tax Policy Shocks: Theory and Empirical Evidence," 2008 Meeting Papers 575, Society for Economic Dynamics.
    11. Ravn, Morten O & Schmitt-Grohé, Stephanie & Uribe, Martín, 2007. "Explaining the Effects of Government Spending Shocks on Consumption and the Real Exchange Rate," CEPR Discussion Papers 6541, C.E.P.R. Discussion Papers.
    12. Lanne, Markku & Lütkepohl, Helmut & Maciejowska, Katarzyna, 2010. "Structural vector autoregressions with Markov switching," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 121-131, February.
    13. Lanne, Markku & Lütkepohl, Helmut, 2010. "Structural Vector Autoregressions With Nonnormal Residuals," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 159-168.
    14. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    15. Jon Faust, 1998. "The robustness of identified VAR conclusions about money," International Finance Discussion Papers 610, Board of Governors of the Federal Reserve System (U.S.).
    16. Andreas Beyer & Roger E.A. Farmer, 2006. "Identification Problems in SDGE Models with an illustration to a small Macro model," Computing in Economics and Finance 2006 81, Society for Computational Economics.
    17. Marco Del Negro & Frank Schorfheide, 2004. "Priors from General Equilibrium Models for VARS," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(2), pages 643-673, May.
    18. Ingram, Beth F. & Whiteman, Charles H., 1994. "Supplanting the 'Minnesota' prior: Forecasting macroeconomic time series using real business cycle model priors," Journal of Monetary Economics, Elsevier, vol. 34(3), pages 497-510, December.
    19. Harald Uhlig, 1997. "Bayesian Vector Autoregressions with Stochastic Volatility," Econometrica, Econometric Society, vol. 65(1), pages 59-74, January.
    20. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    21. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    22. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 63-84, Suppl. De.
    23. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    24. Troy Davig & Eric M. Leeper, 2007. "Fluctuating Macro Policies and the Fiscal Theory," NBER Chapters,in: NBER Macroeconomics Annual 2006, Volume 21, pages 247-316 National Bureau of Economic Research, Inc.
    25. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    26. Juan Francisco Rubio-Ramírez & Daniel F. Waggoner & Tao Zha, 2005. "Markov-switching structural vector autoregressions: theory and application," FRB Atlanta Working Paper 2005-27, Federal Reserve Bank of Atlanta.
    27. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, September.
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    Cited by:

    1. Renou, Ludovic & Schlag, Karl H., 2010. "Minimax regret and strategic uncertainty," Journal of Economic Theory, Elsevier, vol. 145(1), pages 264-286, January.
    2. DeMarzo, Peter M. & Kremer, Ilan & Mansour, Yishay, 2016. "Robust option pricing: Hannan and Blackwell meet Black and Scholes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 410-434.
    3. Raghu Suryanarayanan, 2006. "A Model of Anticipated Regret and Endogenous Beliefs," CSEF Working Papers 161, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 01 Dec 2008.
    4. Takashi Hayashi, 2011. "Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret," Theory and Decision, Springer, vol. 70(4), pages 399-430, April.
    5. Hayashi, Takashi, 2008. "Regret aversion and opportunity dependence," Journal of Economic Theory, Elsevier, vol. 139(1), pages 242-268, March.

    More about this item


    Monopoly; Optimal Pricing; Regret; Robustness;

    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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