Assignment Problems with Complementarities

49 Pages Posted: 28 Sep 2014 Last revised: 23 Nov 2015

See all articles by Thanh Nguyen

Thanh Nguyen

Purdue University - Krannert School of Management

Ahmad Peivandi

Georgia State University - Risk Management & Insurance Department

Rakesh Vohra

University of Pennsylvania - Department of Economics

Date Written: November 1, 2015

Abstract

The problem of allocating bundles of indivisible objects without transfers arises in the assignment of courses to students, of computing resources like CPU time, memory and disk space to computing tasks and the truck loads of food to food banks. In these settings the complementarities in preferences are small compared with the size of the market. We exploit this to design mechanisms satisfying efficiency, envy-freeness and asymptotic strategy-proofness.

Informally, we assume that agents do not want bundles that are too large. There will be a parameter k such that the marginal utility of any item relative to a bundle of size k or larger is zero. We call such preferences k-demand preferences. Given this parameter we show how to represent probability shares over bundles as lotteries over approximately (deterministic) feasible integer allocations. The degree of infeasibility in these integer allocations will be controlled by the parameter k. In particular, ex-post, no good is over allocated by at most k-1 units.

Keywords: Fair Allocation, Indivisible Goods

JEL Classification: C61, D63, D47

Suggested Citation

Nguyen, Thanh and Peivandi Karizbodaghi, Ahmad and Vohra, Rakesh, Assignment Problems with Complementarities (November 1, 2015). PIER Working Paper No. 14-030. Available at SSRN: https://ssrn.com/abstract=2500954 or http://dx.doi.org/10.2139/ssrn.2500954

Thanh Nguyen

Purdue University - Krannert School of Management ( email )

1310 Krannert Building
West Lafayette, IN 47907-1310
United States

Ahmad Peivandi Karizbodaghi

Georgia State University - Risk Management & Insurance Department ( email )

P.O. Box 4036
Atlanta, GA 30302-4036
United States

Rakesh Vohra (Contact Author)

University of Pennsylvania - Department of Economics ( email )

Ronald O. Perelman Center for Political Science
133 South 36th Street
Philadelphia, PA 19104-6297
United States

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