Abstract The Shapley value is one of the most important solution concepts in cooperative game theory, it satisfies uniqueness and fairness properties while its main drawback lies in its high computational complexity. A number of approximation methods have been provided to overcome such intractability. Monte Carlo type methods are the most general and practical approaches approximating the Shapley value thanks to coalitions sampling. Their efficiency depends on the associated sampling and approximation steps. Most of the contributions focus on the sampling step that suffers from a loss of information and the difficulty to deliver a value satisfying certain expected properties such as efficiency and monotonicity. In this paper, we propose an improvement of the approximation step. It associates a Bayesian approach to that of Monte Carlo, to derive a Shapley value approximation, preserving certain expected properties essential for handling real-world applications. We develop our approach for a class of games with binary marginal contributions. We apply it for the calculation of the Shapley value for the weighted voting and bin packing games.

中文翻译：

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用于计算 Shapley 值的贝叶斯蒙特卡罗方法：应用于加权投票和装箱游戏

摘要 沙普利值是合作博弈论中最重要的解概念之一，它满足唯一性和公平性，但主要缺点是计算复杂度高。已经提供了许多近似方法来克服这种难以处理的问题。由于联合采样，蒙特卡罗方法是最通用和最实用的近似 Shapley 值的方法。它们的效率取决于相关的采样和近似步骤。大多数贡献集中在遭受信息丢失和难以提供满足某些预期属性（例如效率和单调性）的值的采样步骤上。在本文中，我们提出了近似步骤的改进。它将贝叶斯方法与蒙特卡罗方法联系起来，推导出 Shapley 值近似值，保留处理实际应用程序所必需的某些预期属性。我们为一类具有二元边际贡献的游戏开发了我们的方法。我们将其应用于加权投票和装箱游戏的 Shapley 值的计算。