In a game-theoretic framework, given parametric agent utility functions, we solve the inverse problem of computing the feasible set of utility function parameters for each individual agent, given that they play a correlated equilibrium strategy. We model agents as utility maximizers, then cast the problem of computing the parameters of players' utility functions as a linear program using the fact that their play results in a correlated equilibrium. We focus on situations where agents must make tradeoffs between multiple competing components within their utility function. We test our method first on a simulated game of Chicken-Dare, and then on data collected in a real-world trial of a mobile fitness game in which five players must balance between protecting their privacy and receiving a reward for burning calories and improving their physical fitness. Through the learned utility functions from the fitness game, we hope to gain insight into the relative importance each user places on safeguarding their privacy vs. achieving the other desirable objectives in the game.