Limited lookahead has been studied for decades in perfect-information games. This paper initiates a new direction via two simultaneous deviation points: generalization to imperfect-information games and a game-theoretic approach. The question of how one should act when facing an opponent whose lookahead is limited is studied along multiple axes: lookahead depth, whether the opponent(s), too, have imperfect information, and how they break ties. We characterize the hardness of finding a Nash equilibrium or an optimal commitment strategy for either player, showing that in some of these variations the problem can be solved in polynomial time while in others it is PPAD-hard or NP-hard. We proceed to design algorithms for computing optimal commitment strategies for when the opponent breaks ties 1) favorably, 2) according to a fixed rule, or 3) adversarially. The impact of limited lookahead is then investigated experimentally. The limited-lookahead player often obtains the value of the game if she knows the expected values of nodes in the game tree for some equilibrium, but we prove this is not sufficient in general. Finally, we study the impact of noise in those estimates and different lookahead depths. This uncovers a lookahead pathology.

中文翻译：

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不完美信息游戏中的有限前瞻

在完美信息博弈中，有限的前瞻已经研究了几十年。本文通过两个同时发生的偏差点启动了一个新方向：对不完美信息博弈的泛化和博弈论方法。当面对一个前瞻受限的对手时应该如何行动的问题是沿着多个轴进行研究的：前瞻深度、对手是否也有不完善的信息，以及他们如何打破联系。我们描述了为任一参与者寻找纳什均衡或最佳承诺策略的难度，表明在这些变体中的一些变体中，问题可以在多项式时间内解决，而在其他变体中，它是 PPAD-hard 或 NP-hard。我们继续设计算法来计算当对手打破平局时的最佳承诺策略 1) 有利地，2) 根据固定规则，或 3) 对抗性的。然后通过实验研究有限前瞻的影响。如果有限前瞻玩家知道某个均衡的博弈树中节点的期望值，她通常会获得博弈的价值，但我们证明这通常是不够的。最后，我们研究了这些估计和不同前瞻深度中噪声的影响。这揭示了前瞻病理。