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Revenue Maximization in the Dynamic Knapsack Problem

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  • Deniz Dizdar
  • Alex Gershkov
  • Benny Moldovanu

Abstract

We analyze maximization of revenue in the dynamic and stochastic knapsack problem where a given capacity needs to be allocated by a given deadline to sequentially arriving agents. Each agent is described by a two-dimensional type that reflects his capacity requirement and his willingness to pay per unit of capacity. Types are private information. We first characterize implementable policies. Then we solve the revenue maximization problem for the special case where there is private information about per-unit values, but capacity needs are observable. After that we derive two sets of additional conditions on the joint distribution of values and weights under which the revenue maximizing policy for the case with observable weights is implementable, and thus optimal also for the case with two-dimensional private information. In particular, we investigate the role of concave continuation revenues for implementation. We also construct a simple policy for which per-unit prices vary with requested weight but not with time, and prove that it is asymptotically revenue maximizing when available capacity/ time to the deadline both go to infinity. This highlights the importance of nonlinear as opposed to dynamic pricing.

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Bibliographic Info

Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp544.

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Length: 36 pages
Date of creation: Apr 2010
Date of revision:
Handle: RePEc:huj:dispap:dp544

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  1. Blackorby, Charles & Dezsö Szalay, 2007. "Multidimensional Screening, Affiliation, and Full Separation," The Warwick Economics Research Paper Series (TWERPS) 802, University of Warwick, Department of Economics.
  2. Jason D. Papastavrou & Srikanth Rajagopalan & Anton J. Kleywegt, 1996. "The Dynamic and Stochastic Knapsack Problem with Deadlines," Management Science, INFORMS, INFORMS, vol. 42(12), pages 1706-1718, December.
  3. Jehiel, Phillipe & Moldovanu, Benny & Stacchetti, E., 1997. "Multidimensional Mechanism Design for Auctions with Externalities," Sonderforschungsbereich 504 Publications 97-04, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  4. Guillermo Gallego & Garrett van Ryzin, 1994. "Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons," Management Science, INFORMS, INFORMS, vol. 40(8), pages 999-1020, August.
  5. Kittsteiner, Thomas & Moldovanu, Benny, 2004. "Priority Auctions and Queue Disciplines that Depend on Processing Time," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 5, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  6. Alex Gershkov & Benny Moldovanu, 2009. "Dynamic Revenue Maximization with Heterogeneous Objects: A Mechanism Design Approach," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 168-98, August.
  7. Garud Iyengar & Anuj Kumar, 2008. "Optimal procurement mechanisms for divisible goods with capacitated suppliers," Review of Economic Design, Springer, Springer, vol. 12(2), pages 129-154, June.
  8. Che, Yeon-Koo & Gale, Ian, 2000. "The Optimal Mechanism for Selling to a Budget-Constrained Buyer," Journal of Economic Theory, Elsevier, vol. 92(2), pages 198-233, June.
  9. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, Econometric Society, vol. 64(1), pages 51-75, January.
  10. S. Christian Albright, 1974. "Optimal Sequential Assignments with Random Arrival Times," Management Science, INFORMS, INFORMS, vol. 21(1), pages 60-67, September.
  11. Gabriel R. Bitran & Susana V. Mondschein, 1997. "Periodic Pricing of Seasonal Products in Retailing," Management Science, INFORMS, INFORMS, vol. 43(1), pages 64-79, January.
  12. 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, INFORMS, vol. 49(10), pages 1287-1309, October.
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Cited by:
  1. Ensthaler, Ludwig & Giebe, Thomas, 2014. "Bayesian optimal knapsack procurement," European Journal of Operational Research, Elsevier, Elsevier, vol. 234(3), pages 774-779.
  2. Gershkov, Alex & Moldovanu, Benny, 2012. "Dynamic allocation and pricing: A mechanism design approach," International Journal of Industrial Organization, Elsevier, Elsevier, vol. 30(3), pages 283-286.

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