Research on Pricing of Data Based on Bi-level Programming Model

Effective value measurement and pricing methods can greatly promote the healthy development of data sharing, exchange and reuse. However, the uncertainty of data value and neglect of interactivity lead to information asymmetry in the transaction process. A perfect pricing system and well-designed data trading market (hereafter called data market) can widely promote data transactions. We take the three-agents data market as an example to construct a sound data trading process. The data owner who provides data records, the model buyer who is interested in buying machine learning (ML) model instances, and the data broker who interacts between the data owner and the model buyer. Based on the characteristics of data market, like truthfulness, revenue maximization, version control, fairness and non-arbitrage, we propose a data pricing methods based on different model versions. Firstly, we utilize market research and construct a revenue maximization (RM) problem to price the different versions of ML models and solve it with the RM-ILP process. However, the RM model based on market research has two major problems: one is that the model buyer has no incentive to tell the truth, that is, the model buyer will lie in the market research to obtain a lower model price; the other is that it asks the data broker to release version menu in advance, resulting in an inefficient operation of the data market. In view of the defects of the RM transaction model, we propose a model buyers behavior analysis, establish the revenue maximization function based on different data versions to establish a bi-level linear programming model. We further add the incentive compatibility constraint and the individual rationality constraint, taking the utility of the model buyer and the revenue of the data broker into account. This reflects the consumer driven model in the data transaction mode. Finally, the RM-BLP process is proposed to transform RM problem into an equivalent single-level integer programming problem and we solve it with the “Gurobi” solver. The validity of the model is verified by experiments. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.