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The Dynamic Assignment of Heterogenous Objects: A Mechanism Design Approach

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  • Gershkov, Alex
  • Moldovanu, Benny

Abstract

We study the allocation of several heterogenous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially according to a Poisson or renewal process. We analyze and compare the policies that maximize either welfare or revenue. We focus on two cases: 1. There is a deadline after which no more objects can be allocated; 2. The horizon is potentially infinite and there is time discounting. We first characterize all implementable allocation schemes, and we compute the expected revenue for any implementable, deterministic and Markovian allocation policy. These properties are shared by the welfare and revenue maximizing policies. Moreover, we show that these policies do not depend on the characteristics of the available objects at each point in time. The revenue-maximizing allocation scheme is obtained by a variational argument which sheds somewhat more light on its properties than the usual dynamic programming approach. We also obtain several properties of the welfare maximizing policy using stochastic dominance measures of increased variability and majorization arguments. These results yield upper/lower bounds on efficiency/revenue for large classes of distributions of agents' characteristics or of distributions of inter-arrival times for which explicit solutions cannot be obtained in closed form.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 6439.

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Date of creation: Aug 2007
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Handle: RePEc:cpr:ceprdp:6439

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Keywords: dynamic pricing; mechanism design; revenue management; sequential assignment;

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  1. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, vol. 40(8), pages 999-1020, August.
  2. Michael A. Arnold & Steven A. Lippman, 2001. "The analytics of search with posted prices," Economic Theory, Springer, vol. 17(2), pages 447-466.
  3. Wedad Elmaghraby & P{\i}nar Keskinocak, 2003. "Dynamic Pricing in the Presence of Inventory Considerations: Research Overview, Current Practices, and Future Directions," Management Science, INFORMS, vol. 49(10), pages 1287-1309, October.
  4. Gabriel R. Bitran & Susana V. Mondschein, 1997. "Periodic Pricing of Seasonal Products in Retailing," Management Science, INFORMS, vol. 43(1), pages 64-79, January.
  5. Das Varma, Gopal & Vettas, Nikolaos, 2001. "Optimal dynamic pricing with inventories," Economics Letters, Elsevier, vol. 72(3), pages 335-340, September.
  6. Susan Athey & Ilya Segal, 2007. "An Efficient Dynamic Mechanism," Levine's Bibliography 122247000000001134, UCLA Department of Economics.
  7. Dirk Bergemann & Juuso Välimäki, 2006. "Efficient Dynamic Auctions," Levine's Bibliography 321307000000000580, UCLA Department of Economics.
  8. S. Christian Albright, 1974. "Optimal Sequential Assignments with Random Arrival Times," Management Science, INFORMS, vol. 21(1), pages 60-67, September.
  9. Gabriel Bitran & René Caldentey, 2003. "An Overview of Pricing Models for Revenue Management," Manufacturing & Service Operations Management, INFORMS, vol. 5(3), pages 203-229, August.
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