Stable Outcomes of Generic Games in Extensive Form

Abstract

Mertens' (1989) definition of stability for a game in strategic form is applied to a game in extensive form with perfect recall. 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 Hillas (1990), yield the same outcomes. In proving this result it is convenient, as a practical matter, to work with enabling strategies, which are like behavioral strategies, instead of mixed strategies. A corollary yields a computational test that usually suffices to identify the stable outcomes of such a game.

Keywords: economic theory, game theory, extensive form, generic, stableset, computation

JEL Classification: C72