Perfect equilibrium and lexicographic beliefs

We extend the results of Blume, Brandenberger, and Dekel to obtain a finite characterization of perfect equlibria in terms of lexicographic probability systems (LPSs). The LPSs we consider are defined over individual strategy sets and thus capture the property of independence among players' actions. Our definition of a product LPS over joint actions of the players is shown to be canonical, in the sense that any independent LPS on joint actions is essentially equivalent to a product LPS according to our definition.