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Optimal Search, Learning and Implementation

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  • Alex Gershkov
  • Benny Moldovanu

Abstract

We characterize the incentive compatible, constrained efficient policy ("second-best") in a dynamic matching environment, where impatient, privately informed agents arrive over time, and where the designer gradually learns about the distribution of agents' values. We also derive conditions on the learning process ensuring that the complete-information, dynamically efficient allocation of resources ("first-best") is incentive compatible. Our analysis reveals and exploits close, formal relations between the problem of ensuring implementable allocation rules in our dynamic allocation problems with incomplete information and learning, and between the classical problem, posed by Rothschild [19], of finding optimal stopping policies for search that are characterized by a reservation price property .

Suggested Citation

  • Alex Gershkov & Benny Moldovanu, 2010. "Optimal Search, Learning and Implementation," Discussion Paper Series dp543, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp543
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    References listed on IDEAS

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    1. Rothschild, Michael, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown," Journal of Political Economy, University of Chicago Press, vol. 82(4), pages 689-711, July/Aug..
    2. Ilya Segal, 2003. "Optimal Pricing Mechanisms with Unknown Demand," American Economic Review, American Economic Association, vol. 93(3), pages 509-529, June.
    3. Cyrus Derman & Gerald J. Lieberman & Sheldon M. Ross, 1972. "A Sequential Stochastic Assignment Problem," Management Science, INFORMS, vol. 18(7), pages 349-355, March.
    4. John Riley & Richard Zeckhauser, 1983. "Optimal Selling Strategies: When to Haggle, When to Hold Firm," The Quarterly Journal of Economics, Oxford University Press, vol. 98(2), pages 267-289.
    5. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-1259, September.
    6. Morgan, Peter B, 1985. "Distributions of the Duration and Value of Job Search with Learning," Econometrica, Econometric Society, vol. 53(5), pages 1199-1232, September.
    7. Dirk Bergemann & Juuso Välimäki, 2007. "Dynamic Marginal Contribution Mechanism," Levine's Bibliography 843644000000000300, UCLA Department of Economics.
    8. Ruqu Wang & Yongmin Chen, 1999. "Learning buyers' valuation distribution in posted-price selling," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 417-428.
    9. Bikhchandani, Sushil & Sharma, Sunil, 1996. "Optimal search with learning," Journal of Economic Dynamics and Control, Elsevier, vol. 20(1-3), pages 333-359.
    10. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    11. Thomas Kittsteiner & Benny Moldovanu, 2005. "Priority Auctions and Queue Disciplines That Depend on Processing Time," Management Science, INFORMS, vol. 51(2), pages 236-248, February.
    12. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    13. Partha Dasgupta & Eric Maskin, 2000. "Efficient Auctions," The Quarterly Journal of Economics, Oxford University Press, vol. 115(2), pages 341-388.
    14. S. Christian Albright, 1977. "A Bayesian Approach to a Generalized House Selling Problem," Management Science, INFORMS, vol. 24(4), pages 432-440, December.
    15. Rosenfield, Donald B. & Shapiro, Roy D., 1981. "Optimal adaptive price search," Journal of Economic Theory, Elsevier, vol. 25(1), pages 1-20, August.
    16. Michael Rothschild, 1974. "Searching for the Lowest Price When the Distribution of Prices Is Unknown: A Summary," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 3, number 1, pages 293-294 National Bureau of Economic Research, Inc.
    17. Alex Gershkov & Benny Moldovanu, 2009. "Learning about the Future and Dynamic Efficiency," American Economic Review, American Economic Association, vol. 99(4), pages 1576-1587, September.
    18. Kohn, Meir G. & Shavell, Steven, 1974. "The theory of search," Journal of Economic Theory, Elsevier, vol. 9(2), pages 93-123, October.
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    Citations

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    Cited by:

    1. Bergemann, Dirk & Pavan, Alessandro, 2015. "Introduction to Symposium on Dynamic Contracts and Mechanism Design," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 679-701.
    2. Mierendorff, Konrad, 2016. "Optimal dynamic mechanism design with deadlines," Journal of Economic Theory, Elsevier, vol. 161(C), pages 190-222.
    3. Yizhaq Minchuk & Aner Sela, 2015. "Asymmetric Sequential Search under Incomplete Information," Working Papers 1510, Ben-Gurion University of the Negev, Department of Economics.
    4. Gershkov, Alex & Moldovanu, Benny, 2013. "Non-Bayesian optimal search and dynamic implementation," Economics Letters, Elsevier, vol. 118(1), pages 121-125.
    5. Kruse, Thomas & Strack, Philipp, 2015. "Optimal stopping with private information," Journal of Economic Theory, Elsevier, vol. 159(PB), pages 702-727.
    6. Babaioff, Moshe & Blumrosen, Liad & Roth, Aaron, 2015. "Auctions with online supply," Games and Economic Behavior, Elsevier, vol. 90(C), pages 227-246.
    7. repec:aea:jeclit:v:55:y:2017:i:2:p:493-544 is not listed on IDEAS
    8. repec:the:publsh:2234 is not listed on IDEAS
    9. Minchuk, Yizhaq & Sela, Aner, 2015. "Asymmetric Sequential Search under Incomplete Information," CEPR Discussion Papers 10579, C.E.P.R. Discussion Papers.
    10. Maarten Janssen & Paul Pichler & Simon Weidenholzer, 2009. "Sequential Search with Incompletely Informed Consumers: Theory and Evidence from Retail Gasoline Markets," Vienna Economics Papers 0914, University of Vienna, Department of Economics.

    More about this item

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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