Combinatorial game theory provides results for the class of two-player, deterministic games with perfect information. With the aim of generalizing this theory to the class of non-perfect information games in mind, we introduce and analyze three variants of the game of Nim. In these variants, the opponent only receives partial information on the move executed by the opponent. We model the variants as games in extensive form and compute Nash equilibria for different starting configurations. For one variant, this provides a full characterization of the game. For the other variants, we prove some partial and structural results, but a full characterization remains elusive.

中文翻译：

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尼姆变种

组合博弈论为具有完美信息的两人、确定性博弈类提供了结果。为了将这一理论推广到非完美信息博弈类，我们介绍并分析了 Nim 博弈的三种变体。在这些变体中，对手仅收到有关对手执行移动的部分信息。我们将变体建模为广泛形式的游戏，并为不同的起始配置计算纳什均衡。对于一种变体，这提供了游戏的完整特征。对于其他变体，我们证明了一些部分和结构结果，但完整的表征仍然难以捉摸。