In the ultimatum game two players have to divide a certain amount of money between them. One player is the allocator and proposes a division of the money. The other is the recipient and can either accept or reject the proposed division. If the recipient accepts, the money is divided as proposed. If the recipient rejects, however, both players receive nothing. Purchase decisions could be classified on two basic factors (or dimensions) : involvement and think/feel in the FCB grid model. In this study we studied the influences of the two factors in purchase decisions on the choice of strategy (or propensity to fairness) in the ultimatum game. The empirical study showed that a decision maker chooses rational strategy more frequently when he (or she) is thinkful (or cognitive) in high involvement level.