Higher-Order Optimality Conditions in Set-Valued Optimization with Respect to General Preference Mappings

Area of Science:

• Welfare economics
• Economic theory
• Mathematical economics

Background:

• Existing welfare economics models often rely on utility functions.
• Preference mappings with star-shape properties are crucial in economic modeling.
• The use of cones to define domination structures is a common approach.

Purpose of the Study:

• To develop higher-order necessary conditions for welfare economics models.
• To analyze models where preference mappings exhibit a star-shape property.
• To explore preference representation without utility functions.

Main Methods:

• Formulating conditions using higher-order directional derivatives of multivalued mappings.
• Describing preferences using arbitrary preference sets.
• Investigating satiable preferences.

Main Results:

• Novel higher-order necessary conditions are established for the specified economic model.
• The conditions are applicable to arbitrary preference sets, accommodating satiable preferences.
• The methodology bypasses the need for utility functions and cone-based domination structures.

Conclusions:

• The presented conditions offer a more general framework for welfare economics analysis.
• This approach expands the applicability of necessary conditions to a broader class of preference structures.
• The findings contribute to the theoretical understanding of economic decision-making with complex preferences.