The article compares two different approaches of incorporating probability into coalition logics. One is based on the semantics of games with stochastic transitions and the other on games with the stochastic failures. The work gives an example of a non-trivial property of coalition power for the first approach and a complete axiomatization for the second approach. It turns out that the logical properties of the coalition power modality under the second approach depend on whether the modal language allows the empty coalition. The main technical results for the games with stochastic failures are a strong completeness theorem for the logical system without the empty coalition and an incompleteness theorem which shows that there is no strongly complete logical system in the language with the empty coalition.

中文翻译：

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随机博弈中的战略联盟

本文比较了将概率纳入联盟逻辑的两种不同方法。一种基于随机转换游戏的语义，另一种基于随机失败游戏的语义。该工作给出了第一种方法的联合权力的重要属性和第二种方法的完整公理化的示例。事实证明，第二种方法下的联盟权力模态的逻辑属性取决于模态语言是否允许空联盟。随机失效博弈的主要技术成果是没有空联盟的逻辑系统的强完备性定理和表明有空联盟的语言中不存在强完备逻辑系统的不完备性定理。