Alex Gershkov
- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9780262028400
- eISBN:
- 9780262327732
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262028400.003.0003
- Subject:
- Economics and Finance, Financial Economics
In this chapter the authors study the revenue maximizing allocation of several heterogeneous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially. ...
More
In this chapter the authors study the revenue maximizing allocation of several heterogeneous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially. There is a deadline after which no more objects can be allocated. The authors first characterize implementable allocation schemes, and compute the expected revenue for any implementable, deterministic and Markovian allocation policy. The revenue-maximizing policy is obtained by a variational argument which sheds more light on its properties than the usual dynamic programming approach. Finally, the authors use their main result in order to: a) derive the optimal inventory choice; b) explain empirical regularities about pricing in clearance sales.Less
In this chapter the authors study the revenue maximizing allocation of several heterogeneous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially. There is a deadline after which no more objects can be allocated. The authors first characterize implementable allocation schemes, and compute the expected revenue for any implementable, deterministic and Markovian allocation policy. The revenue-maximizing policy is obtained by a variational argument which sheds more light on its properties than the usual dynamic programming approach. Finally, the authors use their main result in order to: a) derive the optimal inventory choice; b) explain empirical regularities about pricing in clearance sales.
Alex Gershkov
- Published in print:
- 2015
- Published Online:
- May 2016
- ISBN:
- 9780262028400
- eISBN:
- 9780262327732
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262028400.003.0004
- Subject:
- Economics and Finance, Financial Economics
In this chapter the authors characterize the revenue maximizing policy in the dynamic and stochastic knapsack problem where a given capacity needs to be allocated by a given deadline to sequentially ...
More
In this chapter the authors characterize the revenue maximizing policy 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. The authors first characterize implementable policies. Then they solve the revenue maximization problem for the special case where there is private information about per-unit values, but weights are observable. After that they 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. Finally, the authors analyze a simple policy for which per-unit prices vary with requested weight but do not vary with time. Its implementation requirements are similar to those of the optimal policy and it turns out to be asymptotically revenue maximizing when available capacity/ time to the deadline both go to infinity.Less
In this chapter the authors characterize the revenue maximizing policy 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. The authors first characterize implementable policies. Then they solve the revenue maximization problem for the special case where there is private information about per-unit values, but weights are observable. After that they 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. Finally, the authors analyze a simple policy for which per-unit prices vary with requested weight but do not vary with time. Its implementation requirements are similar to those of the optimal policy and it turns out to be asymptotically revenue maximizing when available capacity/ time to the deadline both go to infinity.
