Concurrent game frames are a standard semantic framework for logics of strategic reasoning. Two notions of coalition power can be derived from such frames: alpha powers and actual powers. An alpha power of a coalition is a set of possible futures such that the coalition has an action that forces the resulting future to lie in that set. An actual power of a coalition is a set of possible futures satisfying the following condition: the coalition has an action such that (1) the action forces the resulting future to lie in the set, and (2) every future in the set is compatible with that action. In two papers, Li and Ju argued that standard concurrent game frames rely on three assumptions that may be too strong: seriality, independence of agents, and determinism. They therefore considered eight classes of general concurrent game frames, determined by which of these three properties hold, and studied the corresponding coalition logics. In this paper, assuming two agents, we prove that for actual powers, the eight classes of general concurrent game frames are representable by eight corresponding classes of neighborhood frames. Building on this result, we show that for alpha powers, the same eight classes of general concurrent game frames are likewise representable by eight corresponding classes of neighborhood frames.

翻译：并发博弈框架是战略推理逻辑的标准语义框架。从这类框架可导出两种联盟权力的概念：α权力与实际权力。一个联盟的α权力是指一组可能的未来状态，使得该联盟存在一个行动能强制使结果未来落入该集合。一个联盟的实际权力则指满足以下条件的可能未来状态集合：该联盟存在一个行动使得（1）该行动强制结果未来落入该集合，且（2）集合中的每个未来状态都与该行动相容。在两篇论文中，Li与Ju指出标准并发博弈框架依赖于三个可能过强的假设：连续性、智能体独立性及确定性。因此他们考虑了八类通用并发博弈框架（由这三个性质的满足情况决定），并研究了相应的联盟逻辑。本文在假设存在两个智能体的前提下，证明了对于实际权力，这八类通用并发博弈框架可由八类对应的邻域框架表示。基于此结果，我们进一步证明对于α权力，同样的八类通用并发博弈框架也可由八类对应的邻域框架表示。