We show that neither Peleg’s nor Tadenuma’s well-known axiomatizations of the core by non-emptiness, individual rationality, super-additivity, and max consistency or complement consistency, respectively, hold when only convex rather than balanced TU games are considered, even if anonymity is required in addition. Moreover, we show that the core and its relative interior are the only two solutions that satisfy Peleg’s axioms together with anonymity and converse max consistency on the domain of convex games.

中文翻译：

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一致性，匿名性和凸游戏领域的核心

我们表明，当只考虑凸而不是平衡的TU游戏时，即使匿名，即使没有匿名，也没有分别通过非空性，个体理性，超可加性和最大一致性或补码一致性来进行Peleg和Tadenuma的著名的核心公理化。另外是必需的。此外，我们证明了核心和它的相对内部是满足Peleg的公理以及凸游戏领域的匿名性和逆最大一致性的两个唯一解决方案。