Document Type

Working Paper

Publication Date


Working Paper Number

WP #10034, September 2010 revised October 2010


In games with strategic substitutes (GSS), convergence of the best response dynamic starting from the inf (or sup) of the strategy space is equivalent to global stability (convergence of every adaptive dynamic to the same pure strategy Nash equilibrium). Consequently, in GSS, global stability can be analyzed using a single best response dynamic. Moreover, in GSS, global stability is equivalent to dominance solvability, showing that in this class of games, two different foundations for robustness of predicted outcomes are equivalent, and both can be checked using a single best response dynamic. These equivalences are useful to study stability of equilibria in a variety of applications. Furthermore, in parameterized GSS, under natural conditions, dynamically stable equilibrium selections can be viewed in terms of monotone selections of equilibria. Several examples are provided.

Publication Status

Published in Games and Economic Behavior, Vol. 75 no. 1 (2012): 337-353.

JEL Classification

C70, C72, C62

File Format



29 pages

File Function

This version: October 3, 2010 (First draft: July 2008)

Included in

Economics Commons