A nonzerosum game with perfect information is considered. The new notion of player's "type" is introduced as a vector whose components define its relations to the other players. In the case of equivalent alternatives the decision is made with the help of the relations-vector. A pair consisting of a relations-vector and a strategy (in the usual sense) is called "type-strategy". It is proved that in the case the relation-vectors are common knowledge for all players in the game there exists a unique in the sense of payoffs Nash equilibria. The examples show the dependence of Nash equilibria from player types.