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Dynamic Allocation and PricingA Mechanism Design Approach$
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Alex Gershkov and Benny Moldovanu

Print publication date: 2015

Print ISBN-13: 9780262028400

Published to MIT Press Scholarship Online: May 2016

DOI: 10.7551/mitpress/9780262028400.001.0001

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The Sequential Assignment of Heterogeneous Objects

The Sequential Assignment of Heterogeneous Objects

Chapter:
(p.11) 2 The Sequential Assignment of Heterogeneous Objects
Source:
Dynamic Allocation and Pricing
Author(s):

Alex Gershkov

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262028400.003.0002

In this chapter the authors study the welfare maximizing assignment of several heterogeneous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially according to a Poisson or renewal process. They 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. The authors first characterize all implementable allocation schemes and show that the dynamically efficient allocation falls in this class. They then 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 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. The authors also propose redistribution mechanisms that 1) implement efficient allocation 2) satisfy individual rationality 3) never run a budget deficit 4) may run a budget surplus that vanishes asymptotically.

Keywords:   Efficient sequential assignment, dynamic Vickrey-Clarke-Groves mechanism, majorization

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