Rationalizability, adaptive dynamics, and the correspondence principle in games with strategic substitutes

Abstract

New insights into the theory of games with strategic substitutes (GSS) are developed. These games possess extremal serially undominated strategies that provide bounds on predicted behavior and on limiting behavior of adaptive dynamics, similar to games with strategic complements (GSC). In parameterized GSS, monotone equilibrium selections are dynamically stable under natural conditions, as in parameterized GSC. Dominance solvability in GSS is not equivalent to uniqueness of Nash equilibrium, but is equivalent to uniqueness of simply rationalizable strategies. Convergence of best response dynamics in GSS is equivalent to global convergence of adaptive dynamics, is equivalent to dominance solvability, and implies uniqueness of equilibrium, all in contrast to GSC. In particular, Cournot stability is equivalent to dominance solvability in GSS. The results shed light on predicted behavior, learning, global stability, uniqueness of equilibrium, and dynamic stability of monotone comparative statics in GSS. Several examples are provided.