Rationalizability in General Games

Abstract

In this paper, we present a unified framework to analyze rationalizable strategic behavior in any arbitrary games by using Harsanyi's notion of type. (i) We investigate properties of rationalizability in general games. Specifically, we show that the set of all the rationalizable strategy profiles is the largest rationalizable set in product form. Moreover, we show that the largest rationalizable set can be derived by the (possibly transfinite) iterated elimination of never-best responses (IENBR). In particular, IENBR is a well-defined order-independent procedure. (ii) We investigate the relationship between rationalizability and Nash equilibrium in general games. We provide a sufficient and necessary condition to guarantee no spurious Nash equilibria in the reduced game after the IENBR procedure. (iii) We formulate and prove that rationalizability is the strategic implication of common knowledge of rationality in general games.