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)
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- Brams,S.L. & Kaplan,T.R., 2002.
"Dividing the indivisible : procedures for allocating cabinet ministries to political parties in a parliamentary system,"
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- Steven J. Brams & Todd R. Kaplan, 2002. "Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System," Discussion Papers 0202, Exeter University, Department of Economics.
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- Steven J. Brams & D. Marc Kilgour, 2001. "Competitive Fair Division," Journal of Political Economy, University of Chicago Press, vol. 109(2), pages 418-443, April.
- Eve Ramaekers, 2013.
"Fair allocation of indivisible goods: the two-agent case,"
Social Choice and Welfare,
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- Rudolf Vetschera & D. Kilgour, 2014. "Fair division of indivisible items between two players: design parameters for Contested Pile methods," Theory and Decision, Springer, vol. 76(4), pages 547-572, April.
- 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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