Coalitional games raise a number of important questions from the point of view of computer science, key among them being how to represent such games compactly, and how to efficiently compute solution concepts assuming such representations. Marginal contribution nets (MC-nets), introduced by Ieong and Shoham, are one of the simplest and most influential representation schemes for coalitional games. MC-nets are a rule-based formalism, in which rules take the form pattern → value, where "pattern" is a Boolean condition over agents, and "value" is a numeric value. Ieong and Shoham showed that, for a class of what we will call "basic" MC-nets, where patterns are constrained to be a conjunction of literals, marginal contribution nets permit the easy computation of solution concepts such as the Shapley value. However, there are very natural classes of coalitional game that require an exponential number of such basic MC-net rules. We present read-once MC-nets, a new class of MC-nets that is provably more compact than basic MC-nets, while retaining the attractive computational properties of basic MC-nets. We show how the techniques we develop for read-once MC-nets can be applied to other domains, in particular, computing solution concepts in network flow games on series-parallel networks.
从计算机科学的角度来看,关联游戏提出了许多重要问题,其中关键是如何紧凑地表示此类游戏,以及如何有效地假设这种表示形式来计算解决方案概念。由Ieong和Shoham提出的边际贡献网(MC-nets),是联盟游戏中最简单,最具影响力的表示方案之一。 MC-net是基于规则的形式主义,其中规则采用 pattern I>→ value I>的形式,其中“ pattern I>”是布尔条件代理,“ 值 I>”是一个数字值。 Ieong和Shoham指出,对于一类我们称之为“基本” MC网络的系统,其中模式被约束为文字的结合,边际贡献网络允许轻松地计算诸如Shapley值之类的解决方案概念。但是,存在非常自然的联盟博弈类,需要成倍数量的此类基本MC-net规则。我们提出了一次读取式MC-网络 I>,它是一类新型的MC-网络,被证明比基础MC-网络更紧凑,同时保留了基础MC-网络的诱人计算性能。我们将展示我们为一次读取的MC-net开发的技术如何可以应用于其他领域,尤其是在串行-并行网络上的网络流游戏中的计算解决方案概念。 P>
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