Maximizing a preference relation on complete chains and lattices

Kukushkin, Nikolai S. (2023): Maximizing a preference relation on complete chains and lattices.

Abstract

Maximization of a preference relation on a given family of subsets of its domain defines a choice function. Assuming the domain to be a poset or a lattice, and considering subcomplete chains or sublattices as potential feasible sets, we study conditions ensuring the existence of optima, as well as properties of the choice function conducive to monotone comparative statics. Concerning optimization on chains, quite a number of characterization results are obtained; when it comes to lattices, we mostly obtain sufficient conditions.

• Item Type: MPRA Paper
• Language: English
• Keywords: preference relation; choice function; complete chain; complete lattice; quasisupermodularity; single crossing; monotone selection
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D1 - Household Behavior and Family Economics > D11 - Consumer Economics: Theory

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