HOW PROPER IS SEQUENTIAL EQUILIBRIUM

A strategy profile of a normal form game is proper if and only if it i s quasi-perfect in every extensive form (with that normal form). Thus, properness requires optimality along a sequence of supporting tremble s, while sequentiality only requires optimality in the limit. A decisi on-theoretic implementation of sequential rationality, strategic indep endence respecting equilibrium (SIRE), is defined and compared to prop er equilibrium, using lexicographic probability systems. Finally, we g ive tremble-based characterizations, which do not involve structural f eatures of the game, of the rankings of strategies that underlie prope r equilibrium and SIRE. (C) 1997 Academic Press.