Abstract: In the process of seeking for gamctheoretic solutions, players arc supposed to be rational which means that they all tend to maximize their expected payoffs. However, there is no a definitely definition of rationality in the game theory and the usual assumption of mutual knowledge of individual rationality to be common knowledge is coarse and maybe too strong, especially when the game is finite, in fact, the nested degree of interactive knowledge of individual rationality has a maximal value that we will show. In this paper we formalized the special rationality conditions for each solution algorithm that we modified for the sake of program. One the other hand, we proposed an algorithm-solution in correspondence with strong rationality. Moreover, we showed that iterated announcement of the rationality we defined could arrive exactly at the algorithm-solution, correspondingly.

Key words: Rationality, Algorithm, Common knowledge, Public announcement