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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.

Suggested Citation

  • Deniz Dizdar & Alex Gershkov & Benny Moldovanu, 2010. "Revenue Maximization in the Dynamic Knapsack Problem," Discussion Paper Series dp544, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp544
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    1. Cyrus Derman & Gerald J. Lieberman & Sheldon M. Ross, 1972. "A Sequential Stochastic Assignment Problem," Management Science, INFORMS, vol. 18(7), pages 349-355, March.
    2. 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.
    3. 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 168-198, August.
    4. 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.
    5. S. Christian Albright, 1974. "Optimal Sequential Assignments with Random Arrival Times," Management Science, INFORMS, vol. 21(1), pages 60-67, September.
    6. Gabriel R. Bitran & Susana V. Mondschein, 1997. "Periodic Pricing of Seasonal Products in Retailing," Management Science, INFORMS, vol. 43(1), pages 64-79, January.
    7. 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.
    8. Jason D. Papastavrou & Srikanth Rajagopalan & Anton J. Kleywegt, 1996. "The Dynamic and Stochastic Knapsack Problem with Deadlines," Management Science, INFORMS, vol. 42(12), pages 1706-1718, December.
    9. Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1999. "Multidimensional Mechanism Design for Auctions with Externalities," Journal of Economic Theory, Elsevier, vol. 85(2), pages 258-293, April.
    10. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    11. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    12. Grace Y. Lin & Yingdong Lu & David D. Yao, 2008. "The Stochastic Knapsack Revisited: Switch-Over Policies and Dynamic Pricing," Operations Research, INFORMS, vol. 56(4), pages 945-957, August.
    13. 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.
    14. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    15. Garud Iyengar & Anuj Kumar, 2008. "Optimal procurement mechanisms for divisible goods with capacitated suppliers," Review of Economic Design, Springer;Society for Economic Design, vol. 12(2), pages 129-154, June.
    16. 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.
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    3. Mierendorff, Konrad, 2016. "Optimal dynamic mechanism design with deadlines," Journal of Economic Theory, Elsevier, vol. 161(C), pages 190-222.
    4. Francis Bloch & David Cantala, 2014. "Dynamic Allocation of Objects to Queuing Agents: The Discrete Model," Documents de travail du Centre d'Economie de la Sorbonne 14066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    5. Mallesh M. Pai & Rakesh Vohra, 2013. "Optimal Dynamic Auctions and Simple Index Rules," Mathematics of Operations Research, INFORMS, vol. 38(4), pages 682-697, November.
    6. Jihyeok Jung & Chan-Oi Song & Deok-Joo Lee & Kiho Yoon, 2024. "Optimal Mechanism in a Dynamic Stochastic Knapsack Environment," Papers 2402.14269, arXiv.org.
    7. Jarman, Felix & Meisner, Vincent, 2017. "Ex-post optimal knapsack procurement," Journal of Economic Theory, Elsevier, vol. 171(C), pages 35-63.
    8. Dirk Bergemann & Johannes Horner, 2010. "Should Auctions Be Transparent?," Levine's Working Paper Archive 661465000000000128, David K. Levine.
    9. Francis Bloch & David Cantala, 2017. "Dynamic Assignment of Objects to Queuing Agents," American Economic Journal: Microeconomics, American Economic Association, vol. 9(1), pages 88-122, February.
    10. Ryuji Sano, 2015. "A Dynamic Mechanism Design for Scheduling with Different Use Lengths," KIER Working Papers 924, Kyoto University, Institute of Economic Research.
    11. Dinard van der Laan & Zaifu Yang, 2019. "Efficient Sequential Assignments with Randomly Arriving Multi-Item Demand Agents," Discussion Papers 19/13, Department of Economics, University of York.
    12. Daniel F. Garrett & Alessandro Pavan, 2012. "Managerial Turnover in a Changing World," Journal of Political Economy, University of Chicago Press, vol. 120(5), pages 879-925.
    13. Ryuji Sano, 2017. "A Dynamic Mechanism Design with Overbooking, Different Deadlines, and Multi-unit Demands," KIER Working Papers 963, Kyoto University, Institute of Economic Research.
    14. Ensthaler, Ludwig & Giebe, Thomas, 2014. "Bayesian optimal knapsack procurement," European Journal of Operational Research, Elsevier, vol. 234(3), pages 774-779.
    15. Gershkov, Alex & Moldovanu, Benny, 2012. "Dynamic allocation and pricing: A mechanism design approach," International Journal of Industrial Organization, Elsevier, vol. 30(3), pages 283-286.

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    More about this item

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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