A Characterization Framework for Stable Sets and Their Variants
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| Format: | Preprint |
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2025
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| _version_ | 1866913988590174208 |
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| author | Andrikopoulos, Athanasios Sampanis, Nikolaos |
| author_facet | Andrikopoulos, Athanasios Sampanis, Nikolaos |
| contents | The theory of optimal choice sets offers a well-established solution framework in social choice and game theory. In social choice theory, decision-making is typically modeled as a maximization problem. However, when preferences are cyclic -- as can occur in economic processes -- the set of maximal elements may be empty, raising the key question of what should be considered a valid choice. To address this issue, several approaches -- collectively known as general solution theories -- have been proposed for constructing non-empty choice sets. Among the most prominent in the context of a finite set of alternatives are the Stable Set (also known as the Von Neumann-Morgenstern set) and its extensions, such as the Extended Stable Set, the socially stable set, and the $m$-, and $w$-stable sets. In this paper, we extend the classical concept of the stable set and its major variants - specifically, the extended stable set, the socially stable set, and the $m$- and $w$-stable sets - within the framework of irreflexive binary relations over infinite sets of alternatives. Additionally, we provide a topological characterization for the existence of such general solutions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_09798 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Characterization Framework for Stable Sets and Their Variants Andrikopoulos, Athanasios Sampanis, Nikolaos General Economics Economics The theory of optimal choice sets offers a well-established solution framework in social choice and game theory. In social choice theory, decision-making is typically modeled as a maximization problem. However, when preferences are cyclic -- as can occur in economic processes -- the set of maximal elements may be empty, raising the key question of what should be considered a valid choice. To address this issue, several approaches -- collectively known as general solution theories -- have been proposed for constructing non-empty choice sets. Among the most prominent in the context of a finite set of alternatives are the Stable Set (also known as the Von Neumann-Morgenstern set) and its extensions, such as the Extended Stable Set, the socially stable set, and the $m$-, and $w$-stable sets. In this paper, we extend the classical concept of the stable set and its major variants - specifically, the extended stable set, the socially stable set, and the $m$- and $w$-stable sets - within the framework of irreflexive binary relations over infinite sets of alternatives. Additionally, we provide a topological characterization for the existence of such general solutions. |
| title | A Characterization Framework for Stable Sets and Their Variants |
| topic | General Economics Economics |
| url | https://arxiv.org/abs/2508.09798 |