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Fuzzy extensions of bargaining sets and their existence in cooperative fuzzy games

机译：讨价还价集的模糊扩展及其在合作模糊博弈中的存在

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摘要

Recently, the concept of classical bargaining set given by Aumann and Maschler in 1964 has been extended to fuzzy bargaining set. In this paper, we give a modification to correct some weakness of this extension. We also extend the concept of the Mas-Colell's bargaining set (the other major type of bargaining sets) to its corresponding fuzzy bargaining set. Our main effort is to prove existence theorems for these two types of fuzzy bargaining sets. We will also give necessary and sufficient conditions for these bargaining sets to coincide with the Aubin Core in a continuous superadditive cooperative fuzzy game which has a crisp maximal coalition of maximum excess at each payoff vector. We show that both Aumann-Maschler and Mas-Colell fuzzy bargaining sets of a continuous convex cooperative fuzzy game coincide with its Aubin core.
机译：最近，Aumann和Maschler在1964年提出的经典议价集的概念已扩展到模糊议价集。在本文中，我们进行了修改以纠正此扩展程序的某些弱点。我们还将Mas-Colell议价集（另一种主要的议价集）的概念扩展到其对应的模糊议价集。我们的主要工作是证明这两种类型的模糊议价集的存在性定理。我们还将为这些讨价还价集提供必要和充分的条件，以使其在连续超加和合作模糊博弈中与Aubin核心一致，该博弈在每个收益向量处具有最大超额数的清晰最大联盟。我们表明，连续凸合作模糊博弈的Aumann-Maschler和Mas-Colell模糊讨价还价集与其Aubin核心一致。

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