This chapter revisits the concept of a utility function, first introduced in Chap. 3, from an axiomatic viewpoint. We review the fundamental principles of decision making as axioms that induce the existence of (continuous) utility functions. Since empirical research of decision situations in real life has shown considerable deviations between mathematical rationality and human behavior, we continue with a series of possible explanations by relaxing or dropping individual axioms from the set of fundamental principles, to explain the difference between human behavior and the utility maximization paradigm. This establishes valuable lessons for the construction of games, say if payoff models are constructed from subjective data (interviews, expert estimates, or similar), but also highlights the need to consider individual risk perception and attitude though the utility function design in a game theoretic model.