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Strategic Prompt Pricing for AIGC Services: A User-Centric Approach

Xiang Li, Bing Luo, Jianwei Huang, Yuan Luo

TL;DR

This work tackles prompt pricing for AIGC services by recognizing that users engage in a two-step decision process: selecting a GAI model and determining how many prompts to submit. By introducing a formal notion of prompt ambiguity and an Optimal Prompt Pricing (OPP) algorithm, the authors transform a bi-level pricing problem into tractable subproblems, revealing a non-monotonic relationship between ambiguity and prompt usage. Theoretical results characterize homogeneous and heterogeneous user behaviors and derive closed-form pricing insights, while experiments with a GPT-like model demonstrate significant platform payoff gains (up to 31.72% over baselines). The study highlights the importance of incorporating user strategies into pricing design to improve platform performance and user welfare in AIGC ecosystems.

Abstract

The rapid growth of AI-generated content (AIGC) services has created an urgent need for effective prompt pricing strategies, yet current approaches overlook users' strategic two-step decision-making process in selecting and utilizing generative AI models. This oversight creates two key technical challenges: quantifying the relationship between user prompt capabilities and generation outcomes, and optimizing platform payoff while accounting for heterogeneous user behaviors. We address these challenges by introducing prompt ambiguity, a theoretical framework that captures users' varying abilities in prompt engineering, and developing an Optimal Prompt Pricing (OPP) algorithm. Our analysis reveals a counterintuitive insight: users with higher prompt ambiguity (i.e., lower capability) exhibit non-monotonic prompt usage patterns, first increasing then decreasing with ambiguity levels, reflecting complex changes in marginal utility. Experimental evaluation using a character-level GPT-like model demonstrates that our OPP algorithm achieves up to 31.72% improvement in platform payoff compared to existing pricing mechanisms, validating the importance of user-centric prompt pricing in AIGC services.

Strategic Prompt Pricing for AIGC Services: A User-Centric Approach

TL;DR

This work tackles prompt pricing for AIGC services by recognizing that users engage in a two-step decision process: selecting a GAI model and determining how many prompts to submit. By introducing a formal notion of prompt ambiguity and an Optimal Prompt Pricing (OPP) algorithm, the authors transform a bi-level pricing problem into tractable subproblems, revealing a non-monotonic relationship between ambiguity and prompt usage. Theoretical results characterize homogeneous and heterogeneous user behaviors and derive closed-form pricing insights, while experiments with a GPT-like model demonstrate significant platform payoff gains (up to 31.72% over baselines). The study highlights the importance of incorporating user strategies into pricing design to improve platform performance and user welfare in AIGC ecosystems.

Abstract

The rapid growth of AI-generated content (AIGC) services has created an urgent need for effective prompt pricing strategies, yet current approaches overlook users' strategic two-step decision-making process in selecting and utilizing generative AI models. This oversight creates two key technical challenges: quantifying the relationship between user prompt capabilities and generation outcomes, and optimizing platform payoff while accounting for heterogeneous user behaviors. We address these challenges by introducing prompt ambiguity, a theoretical framework that captures users' varying abilities in prompt engineering, and developing an Optimal Prompt Pricing (OPP) algorithm. Our analysis reveals a counterintuitive insight: users with higher prompt ambiguity (i.e., lower capability) exhibit non-monotonic prompt usage patterns, first increasing then decreasing with ambiguity levels, reflecting complex changes in marginal utility. Experimental evaluation using a character-level GPT-like model demonstrates that our OPP algorithm achieves up to 31.72% improvement in platform payoff compared to existing pricing mechanisms, validating the importance of user-centric prompt pricing in AIGC services.

Paper Structure

This paper contains 28 sections, 14 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. The AIGC Service Process
  4. Stage 1
  5. Stage 2
  6. Modeling of Heterogeneous Users
  7. User's Prompt Behaviors
  8. User's Expected Utility
  9. User's Expected Payoff
  10. Platform's Prompt Pricing Mechanism Design Problem
  11. Heterogeneous Users' Utilization Strategy
  12. The User's Optimal Utilization Strategy
  13. Multiple Users with Heterogeneous Prompt Ambiguities
  14. The User's Optimal Expected Payoff
  15. Platform's Prompt Pricing Mechanism Design
  16. ...and 13 more sections

Figures (8)

  • Figure 1: Framework of AIGC Service Process.
  • Figure 2: Two-stage Stackelberg Game of AIGC Services.
  • Figure 3: Example of User Prompts and Intention.
  • Figure 5: The Optimal Prompt Number $n^*(m^*,p_{m^*},\epsilon)$ of Homogeneous Users with Different Ambiguity $\epsilon$ under $p^*_{m^*}$ in \ref{['eq10']}.
  • Figure 6: The User's Optimal Utilization Strategy.
  • ...and 3 more figures