The undercut procedure: an algorithm for the envy-free division of indivisible items
AbstractWe propose a procedure for dividing indivisible items between two players in which each player ranks the items from best to worst and has no information about the other player’s ranking. It ensures that each player receives a subset of items that it values more than the other player’s complementary subset, given that such an envy-free division is possible. We show that the possibility of one player’s undercutting the other’s proposal, and implementing the reduced subset for himself or herself, makes the proposer “reasonable” and generally leads to an envy-free division, even when the players rank items exactly the same. Although the undercut procedure is manipulable, each player’s maximin strategy is to be truthful. Applications of the undercut procedure are briefly discussed.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 12774.
Date of creation: Jan 2009
Date of revision:
Fair division; allocation of indivisible items; envy-freeness; ultimatum game;
Other versions of this item:
- Steven Brams & D. Kilgour & Christian Klamler, 2012. "The undercut procedure: an algorithm for the envy-free division of indivisible items," Social Choice and Welfare, Springer, vol. 39(2), pages 615-631, July.
- D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
- D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2009-01-24 (All new papers)
- NEP-CBE-2009-01-24 (Cognitive & Behavioural Economics)
- NEP-GTH-2009-01-24 (Game Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- Steven J. Brams & Todd R. Kaplan, 2002.
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0202, Exeter University, Department of Economics.
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- Steven J. Brams & Peter C. Fishburn, 2000. "Fair division of indivisible items between two people with identical preferences: Envy-freeness, Pareto-optimality, and equity," Social Choice and Welfare, Springer, vol. 17(2), pages 247-267.
- Eve Ramaekers, 2013.
"Fair allocation of indivisible goods: the two-agent case,"
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- RAMAEKERS, Eve, . "Fair allocation of indivisible goods: the two-agent case," CORE Discussion Papers RP -2483, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Brams, Steven J. & Kilgour, D. Marc & Klamler, Christian, 2013. "Two-Person Fair Division of Indivisible Items: An Efficient, Envy-Free Algorithm," MPRA Paper 47400, University Library of Munich, Germany.
- Brams, Steven J. & Kilgour, D. Marc & Klamler, Christian, 2014. "An algorithm for the proportional division of indivisible items," MPRA Paper 56587, University Library of Munich, Germany.
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