We consider infinite two-player games played on finite graphs where the winning condition (say for the first player) is given by a regular omega-language. We address issues of optimization in the construction of winning strategies in such games. Two criteria for optimization are discussed: memory size of finite automata that execute winning strategies, and -for games with liveness requests as winning conditions -"waiting times" for the satisfaction of requests. (For the first aspect we report

more »

... work of Holtmann and Löding, for the second on work of Horn, Wallmeier, and the author.)