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

TL;DR

This paper investigates how different update schedules in noisy best-response dynamics affect the efficiency of long-term equilibria, revealing that small noise alone does not guarantee improved outcomes across various schedules.

Contribution

It revises the concepts of price of anarchy and stability for logit-response dynamics, highlighting the impact of update schedules on equilibrium quality.

Findings

Prior dynamics results depend heavily on synchronous updates.

Small noise alone does not improve equilibrium quality under natural schedules.

Different update schedules can significantly influence long-run outcomes.

Abstract

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.