保证有限合作对策核心的有界性
Ensuring the boundedness of the core of games with restricted cooperation
摘要：
核心是一组参与者的合作博弈$N$是最流行的求解概念之一。当合作受到限制时（可行的联盟形成$2^N$的子集$\cF$），核心可能变得无界，这使得它在实践中的使用值得怀疑。我们的建议是通过将定义核心的一些不平等转化为平等（额外的效率约束）来使核心有界。我们解决以下数学问题：我们能找到一个最小的一组不平等的核心，这样，如果变成平等，核心成为有界的？所获得的新芯被称为限制芯。当$\cF$是一个分配格时，我们完全解决了这个问题，并引入了限制Weber集的概念.我们表明，正规集系统的情况下金额或多或少的情况下分配格。我们还研究了弱并封闭系统的情形，并给出了一般情形的一些结果。
英文摘要：
The core of a cooperative game on a set of players $N$ is one of the most popular concept of solution. When cooperation is restricted (feasible coalitions form a subcollection $\cF$ of $2^N$), the core may become unbounded, which makes it usage questionable in practice. Our proposal is to make the core bounded by turning some of the inequalities defining the core into equalities (additional efficiency constraints). We address the following mathematical problem: can we find a minimal set of inequalities in the core such that, if turned into equalities, the core becomes bounded? The new core obtained is called the restricted core. We completely solve the question when $\cF$ is a distributive lattice, introducing also the notion of restricted Weber set. We show that the case of regular set systems amounts more or less to the case of distributive lattices. We also study the case of weakly union-closed systems and give some results for the general case.
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