How Proper is Sequential Equilibrium?, Games and Economic Behavior
A strategy profile of a normal form game is proper if and only if it is quasi-perfect in every extensive form with that normal form (with that normal form). Thus, properness requires optimality along a sequence of supporting trembles, while sequentiality only requires optimality in the limit. A decision-theoretic implementation of sequential rationality, strategic independence respecting equilibrium (SIRE), is defined and compared to proper equilibrium, using lexicographic probability systems. Finally, we give tremble-based characterizations, which do not involve structural features of the game, of the rankings of strategies that underlie proper equilibrium and SIRE.
Jeroen Swinkels, George Mailath, Larry Samuelson
Swinkels, Jeroen, George Mailath, and Larry Samuelson. 1997. How Proper is Sequential Equilibrium?. Games and Economic Behavior. 18: 193-218.