Two-bound core games and the nucleolus

Doudou Gong*, Bas Dietzenbacher, Hans Peters

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)1419-1433
Number of pages15
JournalAnnals of Operations Research
Issue number3
Publication statusPublished - May 2024

JEL classifications

  • c71 - Cooperative Games


  • two-bound core games
  • nucleolus
  • Talmud rule


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