Dall'Aglio, Marco and Maccheroni, Fabio (2007) Disputed Lands. [Working Paper]. Collegio Carlo Alberto. p. 29. Carlo Alberto Notebooks (n. 58).
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In this paper we consider the classical problem of dividing a land among many agents so that everybody is satisfied with the parcel she receives. In the literature, it is usually assumed that all the agents are endowed with cardinally comparable, additive, and monotone utility functions. In many economic and political situations violations of these assumptions may arise. We show how a family of cardinally comparable utility functions can be obtained starting directly from the agents’ preferences, and how a fair division of the land is feasible, without additivity or monotonicity requirements. Moreover, if the land to be divided can be modelled as a finite dimensional simplex, it is possible to obtain envy-free (and a fortiori fair) divisions of it into subsimplexes. The main tool is an extension of a representation theorem of Gilboa and Schmeidler (1989).
|Item Type:||Report / Paper (Working Paper)|
|Research documents and activity classification:||Working Papers > Refereed Working Papers / of international relevance|
|Divisions:||Department of Business and Management|
|Additional Information:||The definitive version of this paper has been published in "Games and Economic Behavior" Volume 66, Issue 1, May 2009, Pages 57-77.|
|Uncontrolled Keywords:||Gender Fair Division, Envy-freeness, Preference Representation.|
|MIUR Scientific Area:||Area 13 - Economics and Statistics > SECS-S/06 Mathematics for Economics, Actuarial Studies and Finance|
|Deposited by:||Maria Teresa Nistico|
|Date Deposited:||22 Nov 2010 12:48|
|Last Modified:||22 Apr 2015 00:13|
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