On the Replication of the Pre-Kernel and Related Solutions

Holger Meinhardt

MPRA Paper from University Library of Munich, Germany

Abstract: Based on results discussed by Meinhardt (2013), which presents a dual characterization of the prekernel by a finite union of solution sets of a family of quadratic and convex objective functions, we could derive some results related to the single-valuedness of the pre-kernel. Rather than extending the knowledge of game classes for which the pre-kernel consists of a single point, we apply a different approach. We select a game from an arbitrary game class with a single pre-kernel element satisfying the non-empty interior condition of a payoff equivalence class, and then establish that the set of related and linear independent games which are derived from this pre-kernel point of the default game replicates this point also as its sole pre-kernel element. Hence, a bargaining outcome related to this pre-kernel element is stable. Furthermore, we establish that on the restricted subset on the game space that is constituted by the convex hull of the default and the set of related games, the pre-kernel correspondence is single-valued, and therefore continuous. In addition, we provide sufficient conditions that preserve the pre-nucleolus property for related games even when the default game has not a single pre-kernel point. Finally, we apply the same techniques to related solutions of the pre-kernel, namely the modiclus and anti-pre-kernel, to work out replication results for them.

Keywords: Transferable Utility Game; Pre-Kernel; Pre-Nucleolus; Anti-Pre-Nucleolus; Modiclus; Uniqueness of the Pre-Kernel; Convex Analysis; Fenchel-Moreau Conjugation; Indirect Function; Stability Analysis. (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2020-08-03
New Economics Papers: this item is included in nep-gth, nep-ore and nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Related works:
Journal Article: On the Replication of the Pre-kernel and Related Solutions (2024)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:102676

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