Loss Functions for Behavioral Game Theory

Behavioral game theorists all use experimental data to evaluate predictive models of human behavior. However, they differ greatly in their choice of loss function for these evaluations, with error rate, negative log-likelihood, cross-entropy, Brier score, and L2 error all being common choices. We attempt to offer a principled answer to the question of which loss functions make sense for this task, formalizing desiderata that we argue loss functions should satisfy. We construct a family of loss functions, which we dub "diagonal bounded Bregman divergences", that satisfy all of these axioms and includes the squared L2 error. In fact, the squared L2 error is the only acceptable loss that is relatively commonly used in practice; we thus recommend its continued use to behavioral game theorists.