The price of anarchy and stability in general noisy best-response dynamics

Logit-response dynamics (Alos-Ferrer and Netzer, Games and Economic Behavior 2010) are a rich and natural class of noisy best-response dynamics. In this work we revise the price of anarchy and the price of stability by considering the quality of long-run equilibria in these dynamics. Our results show that prior studies on simpler dynamics of this type can strongly depend on a synchronous schedule of the players' moves. In particular, a small noise by itself is not enough to improve the quality of equilibria as soon as other very natural schedules are used.