Stable Equilibria—A Reformulation. Part II. Discussion of the Definition, and Further Results

Abstract

This is the sequel of Mertens (1989). We discuss the geometric content of the definition, showing in particular the algebraic distinctions to matter. We provide an equivalent definition that gets rid of the need to use Hausdorff limits, and finally we show that a “decomposition axiom” eliminates most of the algebraic possibilities, leaving only the “p-stable” sets, for p zero or prime.