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

Marcin Studniarski,Anna Michalak

doi:10.1007/s11228-022-00627-2

Marcin Studniarski, Anna Michalak

Open Access

https://doi.org/10.1007/s11228-022-00627-2

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Abstract

We present higher order necessary conditions for a model of welfare economics, where the preference mapping has a star-shape property. We assume that the preferences can be satiable and can be described by an arbitrary preference set, without the use of utility functions. These conditions are formulated in terms of higher-order directional derivatives of multivalued mappings, and the variable domination structure is not given by cones.

Highlights

In economic equilibrium theory and in qualitative game theory, the behavior of economic agents or players is often determined by gereral preference mappings which do not necessarily lead to pre-order relations
We present higher order necessary conditions for a model of welfare economics, where the preference mapping has a star-shape property
Microeconomic theory often assumes a property of nonsatiation, which means that consumers always choose to have more than less of goods

Summary

Introduction

In economic equilibrium theory and in qualitative game theory, the behavior of economic agents or players is often determined by gereral preference mappings which do not necessarily lead to pre-order relations. Microeconomic theory often assumes a property of nonsatiation, which means that consumers always choose to have more than less of goods. This leads to the conclusion that there is no point of satiation. Mas-Collel in [17] was one of the first who considered the compact consumption sets and satiable preferences. He introduced a weaker than Walrasian equlibrium notion, his work started the discussion about the existence of an equilibrium if we do not assume nonsatiable preferences. Afterwards Allouch and Le Van in [1] and [2] provided a weaker nonsatiation assumption to ensure the existence of competitive equilibria (see [18]). Won and Yannelis in [21] generalized all classical equilibrium results to allow for possibly satiable preferences

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