English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we examine the relationship between the flow of the replicatordynamic, the continuum limit of Multiplicative Weights Update, and a game'sresponse graph. We settle an open problem establishing that under thereplicator, sink chain components -- a topological notion of long-run outcomeof a dynamical system -- always exist and are approximated by the sinkconnected components of the game's response graph. More specifically, each sinkchain component contains a sink connected component of the response graph, aswell as all mixed strategy profiles whose support consists of pure profiles inthe same connected component, a set we call the content of the connectedcomponent. As a corollary, all profiles are chain recurrent in games withstrongly connected response graphs. In any two-player game sharing a responsegraph with a zero-sum game, the sink chain component is unique. In two-playerzero-sum and potential games the sink chain components and sink connectedcomponents are in a one-to-one correspondence, and we conjecture that thisholds in all games.

The Replicator Dynamic, Chain Components and the Response Graph