Rationalizability and learning in games with strategic heterogeneity

It is shown that in games of strategic heterogeneity (GSH), where both strategic complements and substitutes are present, there exist upper and lower serially undominated strategies which provide a bound for all other rationalizable strategies. By establishing a connection between learning in a repeated setting and the iterated deletion of strictly dominated strategies, we are able to provide necessary and sufficient conditions for dominance solvability and stability of equilibria. As a corollary, it is shown that only unique equilibria can be (globally) stable. Lastly, we provide conditions under which games that do not exhibit monotone best responses can be analyzed as a GSH. Applications to industrial organization, network games, and crime and punishment are given.