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The Dynamic Assignment of Heterogenous Objects: A Mechanism Design Approach

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  • Gershkov, Alex
  • Moldovanu, Benny

Abstract

We study the allocation of several heterogenous, commonly ranked objects to impatient agents with privately known characteristics who arrive sequentially according to a Poisson or renewal process. We analyze and compare the policies that maximize either welfare or revenue. We 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. We first characterize all implementable allocation schemes, and we compute the expected revenue for any implementable, deterministic and Markovian allocation policy. These properties are shared by the welfare and revenue maximizing policies. Moreover, we show that these policies do not depend on the characteristics of the available objects at each point in time. The revenue-maximizing allocation scheme is obtained by a variational argument which sheds somewhat more light on its properties than the usual dynamic programming approach. We also 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/revenue 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.

Suggested Citation

  • Gershkov, Alex & Moldovanu, Benny, 2007. "The Dynamic Assignment of Heterogenous Objects: A Mechanism Design Approach," CEPR Discussion Papers 6439, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:6439
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    References listed on IDEAS

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    1. Dirk Bergemann & Juuso Valimaki, 2006. "Efficient Dynamic Auctions," Cowles Foundation Discussion Papers 1584, Cowles Foundation for Research in Economics, Yale University.
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    Cited by:

    1. Benny Moldovanu & Alex Gershkov, 2008. "The Trade-off Between Fast Learning and Dynamic Efficiency," 2008 Meeting Papers 348, Society for Economic Dynamics.

    More about this item

    Keywords

    dynamic pricing; mechanism design; revenue management; sequential assignment;

    JEL classification:

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

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