Abstract We study a non-traditional cooperative game where returns from coalitions are nondeterministic. The long-standing concept of core can be generalized to reflect players’ contentment with their allocations. It is now imperative to formalize the restrictions, such as those pertaining to information, on allocations. The latter are also at times more conducive to fractional representations. With probabilistic structures added, nondeterministic returns become random variables, utility functions attain risk-attitude connotations, and the timing of players’ allocation resolutions gains significance. Under various conditions for utility functions, we show how various core concepts of the general game can be related to its traditionally defined auxiliaries. These developments help pave the way for our illustrations, within two distinct settings, that players’ increased risk aversion would promote the formation of the grand coalition.

中文翻译：

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具有不确定回报的合作博弈

摘要 我们研究了一个非传统的合作博弈，其中联盟的回报是不确定的。核心的长期概念可以概括为反映玩家对其分配的满意程度。现在必须正式确定分配的限制，例如与信息有关的限制。后者有时也更有利于分数表示。随着概率结构的加入，不确定性回报成为随机变量，效用函数获得风险态度的内涵，参与者分配决议的时间变得重要起来。 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 在效用函数的各种条件下，我们展示了一般博弈的各种核心概念如何与其传统定义的辅助因素相关联。这些发展有助于为我们的插图铺平道路，在两个不同的环境中，