  Two firms are engaged in a competitive prediction task. Each firm has two
sources of data -- labeled historical data and unlabeled inference-time data --
and uses the former to derive a prediction model, and the latter to make
predictions on new instances. We study data-sharing contracts between the
firms. The novelty of our study is to introduce and highlight the differences
between contracts that share prediction models only, contracts to share
inference-time predictions only, and contracts to share both. Our analysis
proceeds on three levels. First, we develop a general Bayesian framework that
facilitates our study. Second, we narrow our focus to two natural settings
within this framework: (i) a setting in which the accuracy of each firm's
prediction model is common knowledge, but the correlation between the
respective models is unknown; and (ii) a setting in which two hypotheses exist
regarding the optimal predictor, and one of the firms has a structural
advantage in deducing it. Within these two settings we study optimal contract
choice. More specifically, we find the individually rational and Pareto-optimal
contracts for some notable cases, and describe specific settings where each of
the different sharing contracts emerge as optimal. Finally, in the third level
of our analysis we demonstrate the applicability of our concepts in a synthetic
simulation using real loan data.
