论文标题
典型游戏的水平集
The level sets of typical games
论文作者
论文摘要
在不合作的游戏中，玩家不会相互交流。他们唯一的反馈是他们从执行的策略中获得的回报。重要的是要注意，在总收益功能的每个级别集合中，每个玩家的回报都在不变，因此了解这些级别集合的结构在理解非合作性游戏中起着关键作用。该注释是针对专家和非专家的，不仅引入了非合作游戏理论，而且还显示了其与真实代数几何形状的基本联系。我们在这里证明了有关水平集的结构的一般结果，尽管该水平集可能是专家所知道的，但具有有趣的含义，包括我们最近的应用程序，以为“浮游生物的悖论”提供新的数学解释。我们希望鼓励这些相互关联的领域之间的沟通，并刺激相似方向的进一步工作。
In a non-cooperative game, players do not communicate with each other. Their only feedback is the payoff they receive resulting from the strategies they execute. It is important to note that within each level set of the total payoff function the payoff to each player is unchanging, and therefore understanding the structure of these level sets plays a key role in understanding non-cooperative games. This note, intended for both experts and non-experts, not only introduces non-cooperative game theory but also shows its fundamental connection to real algebraic geometry. We prove here a general result about the structure of the level sets, which although likely to be known by experts, has interesting implications, including our recent application to provide a new mathematical explanation for the "paradox of the plankton." We hope to encourage communication between these interrelated areas and stimulate further work in similar directions.
