The theories of Nash noncooperative solutions and of rationalizability intend to describe the same target problem of ex ante individual decision making, but they are distinctively different. We consider what their essential difference is by giving parallel derivations of their resulting outcomes. The derivations pinpoint that the difference is only in the use of quanti…fiers for each player's prediction about the other's possible decisions; the universal quanti…fier for the former and the existential quantifi…er for the latter. Using this difference, we argue that the former is compatible with the free-will postulate for game theory that each player has free will for his decision making, and that for the latter, the interpretation in terms of determinism would be more natural. In the present approach, however, the distinction between decisions and predictions still remains interpretational. For an explicit distinction, we undertake, in the companion paper, a study of those theories in a framework of common knowledge logic.