# in Zero Sum Games does rationalizability imply positive probability attached in optimal strategy?

Is it true that in every finite zero-sum game G, a strategy is rationalizable if and only if it is played with positive probability by some mixed strategy that is optimal in the mixed extension of G?

-
What do you mean by "optimal in the mixed extension of G"? –  Michael Greinecker Mar 17 '12 at 19:38
the mixed strategy is optimal in the sense that the players maxminimize. namely, a maxminimizer for player 1 solves the problem max_x min_y u1(x,y) and a maxminimizer for player 2 solves max_y min_x u2(x,y), where x is a strategy of player 1 and y is a strategy of player 2. –  Rigel Mar 17 '12 at 22:27