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The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes

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  • Eric Budish

Abstract

This paper proposes a new mechanism for combinatorial assignment--for example, assigning schedules of courses to students--based on an approximation to competitive equilibrium from equal incomes (CEEI) in which incomes are unequal but arbitrarily close together. The main technical result is an existence theorem for approximate CEEI. The mechanism is approximately efficient, satisfies two new criteria of outcome fairness, and is strategyproof in large markets. Its performance is explored on real data, and it is compared to alternatives from theory and practice: all other known mechanisms are either unfair ex post or manipulable even in large markets, and most are both manipulable and unfair.

Suggested Citation

  • Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
  • Handle: RePEc:ucp:jpolec:doi:10.1086/664613
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    References listed on IDEAS

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    1. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
    2. Konishi, Hideo & Quint, Thomas & Wako, Jun, 2001. "On the Shapley-Scarf economy: the case of multiple types of indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 1-15, February.
    3. Philip J Reny & Motty Perry, 2006. "Toward a Strategic Foundation for Rational Expectations Equilibrium," Econometrica, Econometric Society, vol. 74(5), pages 1231-1269, September.
    4. Svensson, Lars-Gunnar, 1983. "Large Indivisibles: An Analysis with Respect to Price Equilibrium and Fairness," Econometrica, Econometric Society, vol. 51(4), pages 939-954, July.
    5. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    6. Louis Kaplow & Steven Shavell, 2001. "Any Non-welfarist Method of Policy Assessment Violates the Pareto Principle," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 281-286, April.
    7. Robert L. Graves & Linus Schrage & Jayaram Sankaran, 1993. "An Auction Method for Course Registration," Interfaces, INFORMS, vol. 23(5), pages 81-92, October.
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