How proper is the dominance-solvable outcome?

We examine the conditions under which iterative elimination of weakly dominated strategies refines the set of proper outcomes of a normal-form game. We say that the proper inclusion holds in terms of outcome if the set of outcomes of all proper equilibria in the reduced game is included in the set of all proper outcomes of the original game. We show by examples that neither dominance solvability nor the transference of decision-maker indifference condition (TDI of Marx and Swinkels [1997]) implies proper inclusion. When both dominance solvablility and the TDI condition are satisfied, a positive result arises: the game has a unique stable outcome. Hence, the proper inclusion is guaranteed