Memorandum, Department of Economics, University of Oslo 1999,31
Proper consistency is deﬁned by the properties that each player takes all opponent strategies into account (is cautious) and deems one opponent strategy to be inﬁnitely more likely than another if the opponent prefers the one to the other (respects preferences). When there is common certain belief of proper consistency, a most preferred strategy is properly rationalizable. Any strategy used with positive probability in a proper equilibrium is properly rationalizable. Only strategies that lead to the backward induction outcome is properly rationalizable in the strategic form of a generic perfect information game. Proper rationalizability can be used to test the robustness of inductive procedures.