Inverse modeling of non-cooperative agents via mixture of utilities

We describe a new method of parametric utility learning for non-cooperative, continuous games using a probabilistic interpretation for combining multiple utility functions - thereby creating a mixture of utilities - under non-spherical noise terms. We present an adaptation of mixture of regression models that takes in to account heteroskedasticity. We show the performance of the proposed method by estimating the utility functions of players using data from a social game experiment designed to encourage energy efficient behavior amongst building occupants. Using occupant voting data we simulate the new game defined by the estimated mixture of utilities and show that the resulting forecast is more accurate than robust utility learning methods such as constrained Feasible Generalized Least Squares (cFGLS), ensemble methods such as bagging, and classical methods such as Ordinary Least Squares (OLS).