论文标题
累积游戏：当前玩家是谁？
Cumulative Games: Who is the current player?
论文作者
论文摘要
组合游戏理论（CGT）是游戏理论的一个分支，几乎独立于经济游戏理论（EGT），并且关注2播放器0-SUM游戏的深度数学属性，这些属性是在各种组合结构上定义的。这项工作的目的是奠定基础，以弥合CGT和EGT之间的概念和技术差距，在这里被解释为所谓的广泛表单游戏，以便可以在统一的框架中对其进行处理。更具体地说，我们介绍了一类$ n $玩家，通用游戏，称为累积游戏，可以通过CGT和EGT工具进行分析。我们展示了CGT的两个最基本定义 - 结果函数以及分离的总和运算符 - 自然会扩展到累积游戏类别。结果函数允许在某些限制下进行有效的平衡计算，并且根据某个玩家的优势，析取的总和运算符使我们可以通过游戏定义部分订单。最后，我们表明任何广泛的表单游戏都可以写为累积游戏。
Combinatorial Game Theory (CGT) is a branch of game theory that has developed almost independently from Economic Game Theory (EGT), and is concerned with deep mathematical properties of 2-player 0-sum games that are defined over various combinatorial structures. The aim of this work is to lay foundations to bridging the conceptual and technical gaps between CGT and EGT, here interpreted as so-called Extensive Form Games, so they can be treated within a unified framework. More specifically, we introduce a class of $n$-player, general-sum games, called Cumulative Games, that can be analyzed by both CGT and EGT tools. We show how two of the most fundamental definitions of CGT---the outcome function, and the disjunctive sum operator---naturally extend to the class of Cumulative Games. The outcome function allows for an efficient equilibrium computation under certain restrictions, and the disjunctive sum operator lets us define a partial order over games, according to the advantage that a certain player has. Finally, we show that any Extensive Form Game can be written as a Cumulative Game.
