Characterizing Stability Properties in Games withStrategic Substitutes

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