复制器动态、链组件和响应图
The Replicator Dynamic, Chain Components and the Response Graph
摘要：
在本文中，我们研究之间的关系的流动的复制动态，连续极限的乘法权重更新，和游戏的响应图。我们解决了一个开放的问题，建立下的复制，汇链组件-一个拓扑概念的长期运行的结果的动态系统-总是存在的，并近似由汇连接组件的游戏的响应图。更具体地说，每个sink链组件包含响应图的sink连接组件，以及所有混合策略配置文件，其支持由相同连接组件中的纯配置文件组成，我们称之为连接组件的内容。作为一个推论，所有的配置文件是链经常性的游戏与强连接的反应图。在任何与零和博弈共享响应图的两人博弈中，汇链组件是唯一的。在两人零和势博弈中，汇链分量和汇连通分量是一一对应的，我们推测这在所有博弈中都成立。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
