On the characterization of weighted simple games
On the characterization of weighted simple games
复制标题
加权简单博弈的表征
作者：
J. Freixas;Marc Freixas;Sascha Kurz
本文件具有双重范围。第一个是澄清和证明两个理论在完全不同的领域发展的同构特征：一方面，阈值逻辑，另一方面，简单游戏。这两个理论的主要目的之一是确定一个简单的游戏何时可以表示为加权游戏，这允许一个非常紧凑和容易理解的表示。对于这个问题，六十年代和七十年代的阈值逻辑中发现了深刻的结果。然而，在过去的二十年里，博弈论已经占据了主导地位，并取得了一些新的成果。本文的第二个主要目标是提供一些新的结果在这个问题上，并提出了一些开放的问题和未来的研究。我们得到的结果取决于两个重要的参数的游戏：数量的类型的等价的球员和数量的类型的转移最小的获胜联盟。
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main purposes in both theories is to determine when a simple game is representable as a weighted game, which allows a very compact and easily comprehensible representation. Deep results were found in threshold logic in the sixties and seventies for this problem. However, game theory has taken the lead and some new results have been obtained for the problem in the past two decades. The second and main goal of this paper is to provide some new results on this problem and propose several open questions and conjectures for future research. The results we obtain depend on two significant parameters of the game: the number of types of equivalent players and the number of types of shift-minimal winning coalitions.