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.
Published in Games and Economic Behavior, Vol. 75 no. 1 (2012): 337-353.
C70, C72, C62
This version: October 3, 2010 (First draft: July 2008)
Roy, Sunanda and Sabarwal, Tarun, "Characterizing stability properties in games with strategic substitutes" (2010). Economics Working Papers (2002–2016). 124.