Online Prompt Pricing based on Combinatorial Multi-Armed Bandit and Hierarchical Stackelberg Game

Generation models have shown promising performance in various tasks, making trading around machine learning models possible. In this paper, we aim at a novel prompt trading scenario, prompt bundle trading (PBT) system, and propose an online pricing mechanism. Based on the combinatorial multi-armed bandit (CMAB) and three-stage hierarchical Stackelburg (HS) game, our pricing mechanism considers the profits of the consumer, platform, and seller, simultaneously achieving the profit satisfaction of these three participants. We break down the pricing issue into two steps, namely unknown category selection and incentive strategy optimization. The former step is to select a set of categories with the highest qualities, and the latter is to derive the optimal strategy for each participant based on the chosen categories. Unlike the existing fixed pricing mode, the PBT pricing mechanism we propose is more flexible and diverse, which is more in accord with the transaction needs of real-world scenarios. We test our method on a simulated text-to-image dataset. The experimental results demonstrate the effectiveness of our algorithm, which provides a feasible price-setting standard for the prompt marketplaces.