Myerson first introduced graph-restricted games in order to model the interaction of cooperative players with an underlying communication network. A dedicated solution concept -- the Myerson value -- is perhaps the most important normative solution concept for cooperative games on graphs. Unfortunately, its computation is computationally challenging. In particular, although exact algorithms have been proposed, they must traverse all connected coalitions of the graph of which there may be exponentially many. In this paper, we consider the issue of approximating the Myerson value for arbitrary graphs and characteristic functions. While Monte Carlo approximations have been proposed for the related concept of the Shapley value, their suitability for the Myerson value has not been studied. Given this, we evaluate and compare (both theoretically and empiraclly) three Monte Carlo sampling methods for the Myerson value: conventional method of sampling permutations; a new, hybrid algorithm that combines exact computations and sampling; and sampling of connected coalitions. We find that our hybrid algorithm performs very well and also significantly improves on the conventional methods.

中文翻译：

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逼近迈尔森值的蒙特卡罗技术——理论和实证分析

Myerson 首先引入了图限制游戏，以便对合作玩家与底层通信网络的交互进行建模。一个专门的解决方案概念——迈尔森值——可能是图上合作博弈最重要的规范解决方案概念。不幸的是，它的计算在计算上具有挑战性。特别是，虽然已经提出了精确算法，但它们必须遍历图的所有连接联盟，其中可能有指数级的多个。在本文中，我们考虑逼近任意图和特征函数的迈尔森值的问题。虽然已经针对 Shapley 值的相关概念提出了 Monte Carlo 近似值，但尚未研究它们对 Myerson 值的适用性。鉴于这种，我们评估和比较（理论上和经验上）三种蒙特卡罗采样方法的迈尔森值： 常规采样排列方法；一种新的混合算法，结合了精确计算和采样；和连接联盟的抽样。我们发现我们的混合算法性能非常好，并且显着改进了传统方法。