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Ex-Post Optimal Knapsack Procurement

42 Pages Posted: 14 Jan 2015 Last revised: 19 Nov 2016

Felix Jarman

University of Mannheim; University of Mannheim - School of Economics (VWL)

Vincent Meisner

TU Berlin

Date Written: November 16, 2016

Abstract

We consider a budget-constrained mechanism designer who selects an optimal set of projects to maximize her utility. Projects may differ in their value for the designer, and their cost is private information. In this allocation problem, the quantity of procured projects is endogenously determined by the mechanism. The designer faces ex-post constraints: The participation and budget constraints must hold for each possible outcome, while the mechanism must be strategyproof. We identify settings in which the class of optimal mechanisms has a deferred acceptance auction representation which allows an implementation with a descending-clock auction. Only in the case of symmetric projects do price clocks descend synchronously such that the cheapest projects are implemented. The case in which values or costs are asymmetrically distributed features a novel tradeoff between quantity and quality. The reason is that guaranteeing allocation to the most favorable projects under strategyproofness comes at the cost of a diminished expected number of conducted projects.

Keywords: Mechanism Design, Knapsack, Budget, Procurement, Auction

JEL Classification: D02, D44, D45, D82, H57

Suggested Citation

Jarman, Felix and Meisner, Vincent, Ex-Post Optimal Knapsack Procurement (November 16, 2016). Available at SSRN: https://ssrn.com/abstract=2548543 or http://dx.doi.org/10.2139/ssrn.2548543

Felix Jarman

University of Mannheim ( email )

L7, 3-5
Mannheim, 68131
Germany

University of Mannheim - School of Economics (VWL) ( email )

Mannheim 68131
Germany

Vincent Meisner (Contact Author)

TU Berlin ( email )

Straße des 17
Juni 135
Berlin, 10623
Germany

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