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Existence of maximals via right traces

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  • Quartieri, Federico

Abstract

This paper examines the conditions for the existence of a maximal element of a relation on every nonempty compact subset of its ground set. A preliminary analysis establishes some connections between the maximals of a relation and those of its right trace. Via this analysis, various results of the literature are unified by identifying a common property of their assumptions that concerns the right trace of the transitive closure of the objective relation. Next, a generalization is provided so as to accommodate some relations of interest to economics. Finally, a necessary and sufficient condition is presented for the existence of a maximal on every nonempty compact subset of the ground set of a relation.

Suggested Citation

  • Quartieri, Federico, 2021. "Existence of maximals via right traces," MPRA Paper 107189, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:107189
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    References listed on IDEAS

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    Cited by:

    1. Quartieri, Federico, 2022. "A unified view of the existence of maximals," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    2. Federico Quartieri, 2023. "Undominated Maximals: General Definition and Characterizations," Mathematics, MDPI, vol. 11(18), pages 1-19, September.

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    More about this item

    Keywords

    Maximal element; Existence; Right trace; Transitive closure; Suzumura-consistency.;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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