Abstract
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 to 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 is optimal. Finally, on the third level of our analysis we demonstrate the applicability of our concepts in a synthetic simulation using real loan data.
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Notes
- 1.
E.g., in advertising, identifying the same user on different devices is called cross-device targeting, enabled by “attribution providers” such as AppsFlyer and Singular.
- 2.
Formally, each signal space is a Lebesgue measurable bi-partition of \([0,1]\times \{0,1\}\).
- 3.
The uniformity assumption here is without loss of generality.
- 4.
Notice that the inference-time signal is drawn according to the firm’s posterior, rather than according to some specific true possible world. This is since we are interested in calculating the firms’ equilibrium behaviors, which follow their Bayesian perspective.
- 5.
See also our analysis of a finite data case in Sect. 4.1.
- 6.
We use Pr[1] as shorthand for \(Pr[t=1]\), and omit \(\pi _w,X,x\) when clear from context.
- 7.
In the full version, we include robustness tests where we vary the choice of features, and explain how the practical implementation corresponds to our formal model.
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Gafni, Y., Gradwohl, R., Tennenholtz, M. (2024). Prediction-Sharing During Training and Inference. In: Schäfer, G., Ventre, C. (eds) Algorithmic Game Theory. SAGT 2024. Lecture Notes in Computer Science, vol 15156. Springer, Cham. https://doi.org/10.1007/978-3-031-71033-9_24
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