AbstractIn 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).
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Bibliographic InfoPaper provided by Collegio Carlo Alberto in its series Carlo Alberto Notebooks with number 58.
Length: 25 pages
Date of creation: 2007
Date of revision:
Gender Fair Division; Envy-freeness; Preference Representation.;
Other versions of this item:
- D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
- D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances
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- Erel Segal-Halevi & Shmuel Nitzan, 2014. "Cake Cutting – Fair and Square," Working Papers 2014-01, Department of Economics, Bar-Ilan University.
- Farhad Hüsseinov & Nobusumi Sagara, 2013. "Existence of efficient envy-free allocations of a heterogeneous divisible commodity with nonadditive utilities," Social Choice and Welfare, Springer, vol. 41(4), pages 923-940, October.
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