Two-bound core games and the nucleolus

Doudou Gong (), Bas Dietzenbacher () and Hans Peters
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Doudou Gong: Northwestern Polytechnical University
Bas Dietzenbacher: Maastricht University

Annals of Operations Research, 2024, vol. 336, issue 3, No 4, 1419-1433

Abstract: Abstract This paper introduces the new class of two-bound core games, where the core can be described by a lower bound and an upper bound on the payoffs of the players. Many classes of games turn out to be two-bound core games. We show that the core of each two-bound core game can be described equivalently by the pair of exact core bounds, and study to what extent the exact core bounds can be stretched while retaining the core description. We provide explicit expressions of the nucleolus for two-bound core games in terms of all pairs of bounds describing the core, using the Talmud rule for bankruptcy problems, and study to what extent these expressions are robust against game changes.

Keywords: Two-bound core games; Nucleolus; Talmud rule; C71 (search for similar items in EconPapers)
Date: 2024
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Working Paper: Two-bound core games and the nucleolus (2021)
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DOI: 10.1007/s10479-022-04949-0

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