We utilize graphical representations of Dictator Games which generate rich individual-level data. Our baseline experiment employs budget sets over feasible payoff-pairs. We test these data for consistency with utility maximization, and we recover the underlying preferences for giving (trade-offs between own payoffs and the payoffs of others). Two further experiments augment the analysis. An extensive elaboration employs three-person budget sets to distinguish preferences for giving from social preferences (trade-offs between the payoffs of others). And an intensive elaboration employs step-shaped sets to distinguish between behaviors that are compatible with well-behaved preferences and those compatible only with not well-behaved cases.