The core with random utility and interdependent preferences: Theory and experimental evidence

Experimental analyses of Shapley-Shubik assignment games revealed that the core prediction is biased. The competing hypotheses are that subjects either have interdependent preferences or a limited understanding of outcomes in alternative matches. To evaluate these hypotheses econometrically, we introduce core concepts with random utility perturbations. The 'logit core' converges to a uniform distribution on the original core as noise disappears. With noise, it captures the non-uniform distribution of observations inside and outside the core, and contrary to regression, it predicts robustly out-of-sample. The logit core thus constitutes a conceptual basis for econometric analyses of assignment problems, and by capturing the whole distribution of outcomes, it allows us to extract all information by maximum likelihood methods. Using this approach, we then show that the core's prediction bias results from overstating the subjects' grasp of outcomes in alternative matches, while social preferences are only of minor relevance.