Revenue maximization in the dynamic knapsack problem

Deniz Dizdar*, Alex Gershkov, Benny Moldovanu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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 we prove that it is asymptotically revenue maximizing when available capacity and time to the deadline both go to infinity. This highlights the importance of nonlinear as opposed to dynamic pricing.

Original languageAmerican English
Pages (from-to)157-184
Number of pages28
JournalTheoretical Economics
Issue number2
StatePublished - May 2011


  • Dynamic mechanism design
  • Knapsack
  • Revenue maximization


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