Carfì, David (2008): Optimal boundaries for decisions. Published in: AAPPPhysical, Mathematical, and Natural Sciences , Vol. 86, No. 1 (2008): pp. 111.

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Abstract
In this paper we state and prove some new results about the optimal boundaries. These boundaries (also called Pareto boundaries or efficiency boundaries or maximal/minimal boundaries) are of increasing importance in the applications to Decision Theory and Economics. First of all the Pareto boundaries are the first and most important generalization of the optima of decision constraints. On the other hand, if f is a real functional (utility function) defined on a non empty set X (of choices or economic strategies) and K is a part of X, the determination of the optimal boundaries of the part K, with respect to some preference relation ≤ of X for which the function f is strictly increasing, allows to reduce the optimization problem of finding the minimum of the functional f upon the part K to the problem of finding the minimum of f upon the minimal boundary of K. We note that the minimal boundary of K is, in general, greatly smaller than the initial decision constraint K. An economic application to the Cournot duopoly is presented.
Item Type:  MPRA Paper 

Original Title:  Optimal boundaries for decisions 
Language:  English 
Keywords:  Optimal strategy, Pareto efficiency, cofinality, decision problem, utility function, Cournòt duopoly 
Subjects:  B  History of Economic Thought, Methodology, and Heterodox Approaches > B2  History of Economic Thought since 1925 > B21  Microeconomics G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice; Investment Decisions D  Microeconomics > D7  Analysis of Collective DecisionMaking H  Public Economics > H2  Taxation, Subsidies, and Revenue > H21  Efficiency; Optimal Taxation C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C44  Operations Research; Statistical Decision Theory 
Item ID:  29243 
Depositing User:  DAVID CARFì 
Date Deposited:  09. Mar 2011 06:54 
Last Modified:  12. Feb 2013 17:35 
References:  [1] N. Bourbaki, Elements de Mathe ́matique, The ́orie des Ensembles (Hermann, Paris, 1958) [2] N. Bourbaki, Elements de Mathe ́matique, Topologie generale (Hermann, Paris, 1958) [3] N. Bourbaki, Elements de Mathe ́matique, Integratio`n, Chapitre 2 (Hermann, Paris, 1958) [4] D. Carf`ı, “Differential optimization via Pareto boundaries” (preprint) [5] J. P. Aubin, Mathematical methods of game and economic theory (NorthHolland, Amsterdam, 1982) [6] J. P. Aubin, Optima and equilibria (Springer Verlag, Berlin, 1998) 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/29243 