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. An outcome relation between such sets determines what the Nash equilibria are. 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.

翻译：我们提出布尔观测博弈，这是一类具有不完美信息与定性目标的多玩家有限策略博弈子类。在布尔观测博弈中，每个玩家关联一组仅其自身可观测真值的命题变量，且该玩家控制是否以及向谁披露该真值，但不控制变量的既定固定真值。布尔观测博弈是布尔博弈的推广——布尔博弈是策略博弈中一个经过充分研究的子类，但具有完全信息且每个玩家控制其变量的真值。在布尔观测博弈中，玩家目标描述关于变量的多智能体知识。与经典策略博弈类似，玩家同时选择策略，因此观测博弈兼具不完全信息与不完美信息的特征，需要针对变量不可区分估值集合推演结果集合。此类集合间的结果关系决定了纳什均衡的构成。我们提出多种结果关系，包括一种定性事后均衡变体，并确定了在给定结果关系下保证纳什均衡存在的条件。我们还研究了检验纳什均衡存在性及验证策略组合是否为纳什均衡的复杂度。进一步，我们研究了具有"知晓是否"目标公式的布尔观测博弈子类（其满足性不依赖于变量真值），证明此类布尔观测博弈与布尔博弈之间存在双向对应关系，且两种对应在纳什均衡存在性方面具有精确性。