Games for chromatic numbers of analytic graphs

We define games which characterize countable coloring numbers of analytic graphs on Polish spaces. These games can provide simple verification of the countable chromatic number of certain graphs. We also get a simpler proof of a dichotomy originally proved by Adams and Zapletal: if an analytic graph has an uncountable color number, then it contains a certain subgraph. Joint work with Jindrich Zapletal.