Rationalizability and logical inference

In a model of modal logic it is shown that the assumptions of rationality and intelligence of the players imply that only rationalizable strategies can be played. Nothing more can be inferred from these rules. Hereby the assumption of “intelligence” expresses that whatever an outside observer can deduce about the play of the game can be inferred by the players themselves, provided they have the same information. In our framework the assumption of intelligence is simply the familiar inference rule of necessitation in modal logic. Our approach contrasts with a hierarchical approach traditional in the literature, where assumption about knowledge about knowledge ... about rationality are added one by one.