The class of totally balanced games is a class of transferable-utility coalitional games providing important models of cooperative behavior used in mathematical economics. They coincide with market games of Shapley and Shubik and every totally balanced game is also representable as the minimum of a finite set of additive games. In this paper we characterize the polyhedral cone of totally balanced games by describing its facets. Our main result is that there is a correspondence between facet-defining inequalities for the cone and the class of special balanced systems of coalitions, the so-called irreducible min-balanced systems. Our method is based on refining the notion of balancedness introduced by Shapley. We also formulate a conjecture about what are the facets of the cone of exact games, which addresses an open problem appearing in the literature.

中文翻译：

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完全平衡游戏锥的各个方面

完全平衡博弈是一类可转让的效用联盟博弈，它提供了数学经济学中使用的重要合作行为模型。它们与Shapley和Shubik的市场游戏相吻合，每个完全平衡的游戏也可以表示为有限的加法游戏集的最小值。在本文中，我们通过描述其各个方面来刻画完全平衡游戏的多面锥。我们的主要结果是，圆锥的刻面定义不等式与联盟的特殊平衡系统（即所谓的不可约最小平衡系统）类别之间存在对应关系。我们的方法基于完善Shapley引入的平衡概念。我们还对确切游戏的锥面的各个方面提出了一个猜想，