Pricing Strategies for Different Accuracy Models from the Same Dataset Based on Generalized Hotelling's Law

TL;DR

The paper models a data-trading market where a seller, using a single dataset $D$, retrains multiple models with increasing accuracies $A_i$ at costs $c_i$ and sells them competitively under a generalized Hotelling's law, treating accuracy as a distance in product space. It develops static and dynamic pricing frameworks, including backward-induction pricing, continuity of revenue, dual/quasi-dual formulations, and chain-like Nash equilibria, while connecting market allocations across adjacent models and proving robustness under incomplete information. A key contribution is the enveloping utility construction and the analysis of two-nodes and general-chain scenarios, supported by separable utility specializations with uniform and continuous distributions. The results yield concrete pricing strategies and stability results for data markets, enabling profit optimization for data sellers while ensuring predictable buyer choices and market connectivity, with practical implications for data valuation under model-level competition.

Abstract

We consider a scenario where a seller possesses a dataset $D$ and trains it into models of varying accuracies for sale in the market. Due to the reproducibility of data, the dataset can be reused to train models with different accuracies, and the training cost is independent of the sales volume. These two characteristics lead to fundamental differences between the data trading market and traditional trading markets. The introduction of different models into the market inevitably gives rise to competition. However, due to the varying accuracies of these models, traditional multi-oligopoly games are not applicable. We consider a generalized Hotelling's law, where the accuracy of the models is abstracted as distance. Buyers choose to purchase models based on a trade-off between accuracy and price, while sellers determine their pricing strategies based on the market's demand. We present two pricing strategies: static pricing strategy and dynamic pricing strategy, and we focus on the static pricing strategy. We propose static pricing mechanisms based on various market conditions and provide an example. Finally, we demonstrate that our pricing strategy remains robust in the context of incomplete information games.

Figures (4)

• Figure 1: Generalized Hotelling's law
• Figure 2: Data Chain (Dataset D cannot be directly sold to the market)
• Figure 3: Market allocations(red is for $T_1$ and blue is for $T_2$)
• Figure 4: Dual generalized Hotelling's law

Theorems & Definitions (18)

• Definition 2.1
• Remark 2.2
• Definition 3.1
• Lemma 3.2
• proof
• Theorem 3.3
• Corollary 3.4
• Corollary 3.5
• Lemma 3.6
• proof