Two-bound core games and the nucleolus
本文提出了一类新的双边界核心博弈，其核心可由玩家收益的下界和上界描述，并给出了核仁的显式表达式，适用于破产问题等场景。
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.