Weak* Dominance

We propose a new dominance notion in strategic games—weak* dominance—that reflects the idea of cautious* rationality, whereby a rational player believes that each opponent’s individual actions are played with positive probabilities. In this paper, we show that an action is weakly* dominated if, and only if, it is not a best response to any marginally full-support conjecture. We characterize Gul’s (1996) notion of perfect τ-rationalizability through an iterative procedure (S∞W*): removing all weakly* dominated actions in the first round, and then removing only strictly dominated actions in the subsequent rounds. Moreover, we provide epistemic foundations for the iterative procedure in a lexicographic type structure model.