Existence of maximals via right traces

Quartieri, Federico (2021): Existence of maximals via right traces.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Maximal element; Existence; Right trace; Transitive closure; Suzumura-consistency.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C60 - General; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; D - Microeconomics > D1 - Household Behavior and Family Economics > D11 - Consumer Economics: Theory

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