Mathematical Sciences: Research into Multilinear Extensions of Games and Applications

游戏的多线性扩展（MLE），首次引入 作为一种计算游戏价值的技术， 在过去的二十年中，已经显示出具有许多其他应用。 在这个项目中，它的数学特性将在 一些细节，着眼于这样的应用， 对称和非对称大值的计算 游戏，衍生其他（不对称）的游戏价值，开发 解决方案的概念，游戏没有方支付，计算 缩小游戏 MLE也可以用来解决某些问题， 在当前某些类型的游戏中发现。 其中包括非原子游戏，用于代表 纯粹竞争的经济状况，以及空间博弈， 经常被用来模拟投票和联盟的形成， 政治局势。 在这两种情况下，目前 表示无法允许在 代理的一部分; MLE（具有概率 解释）可以弥补这个缺点。

The multilinear extension (MLE) of a game, first introduced as a technique for calculating the value of a game, has over the past two decades been shown to have numerous other applications. In this project its mathematical properties will be studied in some detail, with a view towards such applications as the computation of both symmetric and asymmetric values of large games, deriving other (asymmetric) values to games, developing solution concepts for games without side payments, and computing reduced games. MLE may also be used to resolve certain problems which are found in the current representation of some types of games. These include non-atomic games, which are used to represent economic situations of pure competition, and spatial games, which are frequently used to model voting and coalition formation in political situations. In both of these cases, the current representation fails to allow for some stochastic behavior on the part of agents; the MLE (which has a probabilistic interpretation) can remedy this drawback.