This paper investigates the belief structure in the ultimatum bargaining game to test whether people care only about the pecuniary payoffs. In the normal-form quantal response equilibrium model, the responder's choice is made taking the proposer's intention into account while is independent in the agent normal-form game. Using Slonim and Roth's (1998, Econometrica) experimental data, it is shown that the experimental subjects who played the role of the responder cared not only the pecuniary payoffs but also the fairness of the amount of offers.