论文标题
复制器动态，链组件和响应图
The Replicator Dynamic, Chain Components and the Response Graph
论文作者
论文摘要
在本文中，我们检查了复制器动态流的流量，乘法权重更新的连续限制与游戏的响应图之间的关系。我们解决了一个开放的问题，确定在复制器下，水槽链组件（一个动态系统的长期结果的拓扑概念）始终存在，并由游戏响应图的接收器连接组件近似。更具体地说，每个接收器链组件都包含响应图的接收器连接组件，以及所有混合策略配置文件，其支持由同一连接的组件中的纯轮廓组成，我们称之为连接组件的内容。作为推论，所有配置文件均在具有牢固连接的响应图的游戏中经常出现。在与零和零游戏共享响应图的任何两个玩家游戏中，水槽链组件是唯一的。在两人零和潜在游戏中，水槽链组件和接收器连接的组件是一对一的信件，我们猜想这在所有游戏中都具有。
In this paper we examine the relationship between the flow of the replicator dynamic, the continuum limit of Multiplicative Weights Update, and a game's response graph. We settle an open problem establishing that under the replicator, sink chain components -- a topological notion of long-run outcome of a dynamical system -- always exist and are approximated by the sink connected components of the game's response graph. More specifically, each sink chain component contains a sink connected component of the response graph, as well as all mixed strategy profiles whose support consists of pure profiles in the same connected component, a set we call the content of the connected component. As a corollary, all profiles are chain recurrent in games with strongly connected response graphs. In any two-player game sharing a response graph with a zero-sum game, the sink chain component is unique. In two-player zero-sum and potential games the sink chain components and sink connected components are in a one-to-one correspondence, and we conjecture that this holds in all games.
