Game theory has become a standard tool for depicting and demonstrating various game-like phenomena by providing appropriate mathematical models and for analyzing and predicting agents' behaviors and their decisions by formalizing solution concepts. The conventional game model mainly concerns ideal systems that would always guarantee optimal responses, which appears unrealistic for practical game scenarios since decision-making usually entails resource costs. Therefore, this study considers players' decision-making in extensive games when the computational cost of searching the strategy space is limited. We start with a new mathematical model of extensive games that features a bound on computational resources during players' decision-making process such that they can only foresee a part of the available alternatives in the future. This model is more appropriate in predicting players' strategies than the conventional model, under which we investigate the effects of computational costs on players' strategies as well as the computational complexity. Furthermore, a simulation experiment is performed to seek the connection between the amount of resources and the goodness of the outcomes. This study is expected to provide a foundation for players' rational decision-making with computational costs.

中文翻译：

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通过建模和模拟探索大量游戏中计算成本的影响

博弈论已成为一种标准工​​具，通过提供适当的数学模型来描述和展示各种类似游戏的现象，并通过形式化解决方案概念来分析和预测代理的行为及其决策。传统的博弈模型主要涉及始终保证最佳响应的理想系统，这对于实际的博弈场景来说似乎是不切实际的，因为决策通常需要资源成本。因此，本研究考虑了当搜索策略空间的计算成本有限时，玩家在广泛博弈中的决策。我们从广泛游戏的新数学模型开始，该模型在玩家决策过程中对计算资源进行了限制，因此他们只能预见未来可用替代方案的一部分。该模型比传统模型更适合预测参与者的策略，在传统模型下，我们研究计算成本对参与者策略的影响以及计算复杂度。此外，还进行了模拟实验，以寻求资源量与结果优劣之间的联系。该研究有望为玩家在计算成本下的理性决策提供基础。