Abstract

In the paper, we consider conditions providing the coincidence of the cores and superdifferentials of fuzzy cooperative games with side payments. It turned out that weak homogeneity is one of the simplest sufficient conditions. Moreover, by applying the so-called \(S^* \)-representation of a fuzzy game introduced by the author, we show that for any \(v\) with nonempty core \(C(v) \) there exists some game \(u \) such that \(C(v) \) coincides with the superdifferential of \(u \). By applying the subdifferential calculus, we describe a structure of the core for classical fuzzy extensions of the ordinary cooperative game (e.g., the Aubin and Owen extensions) as well as for some new continuations, like the generalized Airport game.

中文翻译：

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模糊$$TU $$-合作博弈的核心和超微分

摘要

在本文中，我们考虑了提供带有边支付的模糊合作博弈的核心和超微分重合的条件。原来，弱同质性是最简单的充分条件之一。此外，通过应用所谓的 \（S ^ * \）由作者引入了模糊的游戏-表示，我们表明，任何\（V \）与非空芯 \（C（V）\）存在一些游戏\(u \)使得\(C(v) \)与\(u \)的超微分重合 . 通过应用次微分，我们描述了普通合作博弈的经典模糊扩展（例如，Aubin 和 Owen 扩展）以及一些新的延续，如广义机场博弈的核心结构。