On the Existence of a Fuzzy Core in an Exchange Economy Full article
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Lecture Notes in Computer Science
ISSN: 0302-9743 , E-ISSN: 1611-3349 |
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| Output data | Year: 2022, Volume: 13367 LNCS, Pages: 210-217 Pages count : 8 DOI: 10.1007/978-3-031-09607-5_15 | ||
| Tags | Edgeworth equilibria; Existence theorems; Fuzzy core; Perfect competition | ||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0019 |
Abstract:
The fuzzy core is widely used in theoretical economics for modeling perfect competition. However, in modern literature, the proof of its existence is presented indirectly and applies a cumbersome construction. It usually is based on the idea of replicated economies, via standard core existence, followed by passing to the limits, allowing the number of replicas tends to infinity. The result is also proved under additional restrictive assumptions. We present a direct proof based on two well-known theorems: Michael’s theorem on the existence of a continuous selector for a point-to-set mapping and Brouwer’s fixed point theorem. This new direct proof is efficient and shortest among others. Moreover, now the existence of a fuzzy core is stated under other weakest assumptions: agent preferences can be incomplete, non-transitive, satiated, and so on. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
Cite:
Marakulin V.
On the Existence of a Fuzzy Core in an Exchange Economy
Lecture Notes in Computer Science. 2022. V.13367 LNCS. P.210-217. DOI: 10.1007/978-3-031-09607-5_15 Scopus OpenAlex
On the Existence of a Fuzzy Core in an Exchange Economy
Lecture Notes in Computer Science. 2022. V.13367 LNCS. P.210-217. DOI: 10.1007/978-3-031-09607-5_15 Scopus OpenAlex
Identifiers:
| Scopus: | 2-s2.0-85134192477 |
| OpenAlex: | W4285196497 |
Citing:
| DB | Citing |
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| OpenAlex | 1 |