Stable Outcomes of Generic Games in Extensive Form

We apply Mertens' dedinition of stability for a game in strategic form to a game in extensive form with perfect recall. We prove that if payoffs are generic then the outcomes of stable sets of equilibria defined via homological essentiality by Mertens coincide with those defined via homotopic essentiality. This implies that for such games various definitions of stability in terms of perturbations of players' strategies as in Mertens or best-reply correspondences as in Govindan and Wilson yield the same outcomes. A corollary yields a computational test that usually suffices to identify the stable outcomes of such a game.