We introduce Boolean Observation Games, a subclass of multi-player finite strategic games with incomplete information and qualitative objectives. In Boolean observation games, each player is associated with a finite set of propositional variables of which only it can observe the value, and it controls whether and to whom it can reveal that value. It does not control the given, fixed, value of variables. Boolean observation games are a generalization of Boolean games, a well-studied subclass of strategic games but with complete information, and wherein each player controls the value of its variables. In Boolean observation games player goals describe multi-agent knowledge of variables. As in classical strategic games, players choose their strategies simultaneously and therefore observation games capture aspects of both imperfect and incomplete information. They require reasoning about sets of outcomes given sets of indistinguishable valuations of variables. What a Nash equilibrium is, depends on an outcome relation between such sets. We present various outcome relations, including a qualitative variant of ex-post equilibrium. We identify conditions under which, given an outcome relation, Nash equilibria are guaranteed to exist. We also study the complexity of checking for the existence of Nash equilibria and of verifying if a strategy profile is a Nash equilibrium. We further study the subclass of Boolean observation games with `knowing whether' goal formulas, for which the satisfaction does not depend on the value of variables. We show that each such Boolean observation game corresponds to a Boolean game and vice versa, by a different correspondence, and that both correspondences are precise in terms of existence of Nash equilibria.

本文提出了布尔观察博弈，研究了其多人有限策略博弈、不完全信息和定性目标等方面，探讨了关于纳什均衡存在性的条件以及验证策略配置是否为纳什均衡的复杂性，并详细研究了只关注知识满足度的布尔观察博弈，并通过两组不同的对应关系精确说明了与布尔博弈的对应关系。

布尔观察游戏