用蒙特卡罗方法逼近迈尔森值--理论与实证分析
Monte Carlo Techniques for Approximating the Myerson Value -- Theoretical and Empirical Analysis
摘要：
迈尔森首先引入了图限制游戏，以模拟合作玩家与底层通信网络的互动。一个专门的解决方案的概念-迈尔森值-也许是最重要的规范解决方案的概念，合作游戏的图。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的算法，他们必须遍历所有连接联盟的图，其中可能有指数许多。本文考虑任意图和特征函数的Myerson值的逼近问题。虽然蒙特卡罗近似已经提出了沙普利值的相关概念，其适用性迈尔森值尚未研究。鉴于此，我们评估和比较（理论上和provisaclly）三个蒙特卡洛抽样方法的迈尔森值：传统的抽样排列的方法，一个新的，混合算法，结合精确的计算和采样;和采样的连接联盟。我们发现，我们的混合算法表现得非常好，也显着提高了传统的方法。
英文摘要：
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.
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