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Optimal boundaries for decisions

Author

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  • Carfì, David

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.

Suggested Citation

  • Carfì, David, 2008. "Optimal boundaries for decisions," MPRA Paper 29243, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:29243
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    File URL: https://mpra.ub.uni-muenchen.de/29243/1/MPRA_paper_29243.pdf
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    Citations

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    Cited by:

    1. David Carfì & Emanuele Perrone, 2013. "Asymmetric Cournot Duopoly: A Game Complete Analysis," Journal of Reviews on Global Economics, Lifescience Global, vol. 2, pages 194-202.
    2. Musolino, Francesco & Carfì, David, 2012. "A game theory model for currency markets stabilization," MPRA Paper 39240, University Library of Munich, Germany.
    3. David CARFI & Caterina FICI, 2012. "The Government-Taxpayer Game," Theoretical and Practical Research in the Economic Fields, ASERS Publishing, vol. 3(1), pages 13-25.
    4. Carfì, David & Musolino, Francesco, 2012. "Game theory and speculation on government bonds," Economic Modelling, Elsevier, vol. 29(6), pages 2417-2426.
    5. Carfì, David & Perrone, Emanuele, 2011. "Asymmetric Bertrand duopoly: game complete analysis by algebra system Maxima," MPRA Paper 35417, University Library of Munich, Germany.
    6. Carfì, David & Musolino, Francesco, 2012. "A coopetitive approach to financial markets stabilization and risk management," MPRA Paper 37098, University Library of Munich, Germany.
    7. Carfì, David, 2009. "Differentiable game complete analysis for tourism firm decisions," MPRA Paper 29193, University Library of Munich, Germany.
    8. Carfí, David & Musolino, Francesco, 2014. "Speculative and hedging interaction model in oil and U.S. dollar markets with financial transaction taxes," Economic Modelling, Elsevier, vol. 37(C), pages 306-319.
    9. Alessia Donato & David Carfì & Beatrice Blandina, 2018. "Coopetitive Games for Management of Marine Transportation Activity: A Study Case," Mathematics, MDPI, vol. 6(12), pages 1-17, December.
    10. Carfì, David & Donato, Alessia & Schilirò, Daniele, 2018. "An environmentally sustainable global economy. A coopetitive model," MPRA Paper 86718, University Library of Munich, Germany.
    11. Carfì, David & Perrone, Emanuele, 2012. "Game complete analysis of symmetric Cournot duopoly," MPRA Paper 35930, University Library of Munich, Germany.

    More about this item

    Keywords

    Optimal strategy; Pareto efficiency; cofinality; decision problem; utility function; Cournòt duopoly;
    All these keywords.

    JEL classification:

    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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