Understanding the properties of games played under computational constraints remains challenging. For example, how do we expect rational (but computationally bounded) players to play games with a prohibitively large number of states, such as chess? This paper presents a novel model for the precomputation (preparing moves in advance) aspect of computationally constrained games. A fundamental trade-off is shown between randomness of play, and susceptibility to precomputation, suggesting that randomization is necessary in games with computational constraints. We present efficient algorithms for computing how susceptible a strategy is to precomputation, and computing an $\epsilon$-Nash equilibrium of our model. Numerical experiments measuring the trade-off between randomness and precomputation are provided for Stockfish (a well-known chess playing algorithm).

中文翻译：

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在计算约束下进行的游戏中的模拟计算

理解在计算约束下玩的游戏的性质仍然具有挑战性。例如，我们如何期望理性的（但在计算上受限制的）玩家玩具有过多状态的游戏，例如国际象棋？本文提出了一种用于计算受限游戏的预计算（预先准备动作）方面的新颖模型。在游戏的随机性和对预计算的敏感性之间显示了一个基本的权衡，这表明在具有计算约束的游戏中，随机化是必要的。我们提出了有效的算法，用于计算策略对预计算的敏感程度，并计算模型的\ epsilon-Nash平衡。