We lay out a model of games with imperfect information that features explicit communication actions, by which the entire observation history of a player is revealed to another player. Such full-information protocols are common in asynchronous distributed systems; here, we consider a synchronous setting with a single active player who may communicate with multiple passive observers in an indeterminate environment. We present a procedure for solving the basic strategy-synthesis problem under regular winning conditions. We present our solution in an abstract framework of games with imperfect information and we split the proof in two conceptual parts: (i) a generic reduction schema from imperfect-information to perfect-information games, and (ii) a specific construction for full-information protocols that satisfies the requirement of the reduction schema. Furthermore we show that the number of passive observers induces a strict hierarchy, both in terms of expressiveness and complexity: with n observers, a full-information protocol can express indistinguishability relations (defining imperfect information for the player in the protocol) that are not expressible with n-1 observers, and the strategy-synthesis problem is (n+1)-EXPTIME-complete.

翻译：我们构建了一个带有显式通信动作的不完美信息博弈模型，通过该模型，玩家的完整观测历史可向另一玩家揭示。此类全信息协议在异步分布式系统中较为常见；本文考虑同步场景，其中单个主动玩家可在不确定环境中与多个被动观察者进行通信。我们提出了一种在正则获胜条件下求解基本策略综合问题的过程。我们在不完美信息博弈的抽象框架中呈现该解法，并将证明分为两个概念性部分：(i) 从不完美信息博弈到完美信息博弈的通用归约模式，以及(ii) 满足归约模式要求的全信息协议特定构造。此外，我们证明被动观察者的数量会引发严格层级结构，无论是在表达能力还是复杂度方面：拥有n个观察者时，全信息协议可表达（n-1）个观察者无法表达的不区分关系（定义协议中玩家的不完美信息），且策略综合问题为（n+1）-EXPTIME完全。