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PACT: A Contract-Theoretic Framework for Pricing Agentic AI Services Powered by Large Language Models

Ya-Ting Yang, Quanyan Zhu

TL;DR

PACT tackles the pricing challenge for agentic AI services powered by LLMs under information asymmetry and multi-dimensional QoS. It introduces a contract-theoretic framework that models QoS with latency and user satisfaction through $q_k = \delta A_k + (1-\delta)(1 - T_k)$ and incorporates liability costs to reflect regulatory risk, while guaranteeing incentive compatibility and individual rationality via a contract menu. The paper shows how to reduce IR/IC constraints using LDIC/LUIC arguments and solves the resulting optimization with a Lagrangian approach, demonstrating via simulations that users select their truthful contracts and that liability considerations influence pricing and QoS levels. This framework supports scalable, accountable pricing for cloud-based agentic AI in high-stakes domains and motivates further work on auditing and liability design to enhance safety and deployment viability.

Abstract

Agentic AI, often powered by large language models (LLMs), is becoming increasingly popular and adopted to support autonomous reasoning, decision-making, and task execution across various domains. While agentic AI holds great promise, its deployment as services for easy access raises critical challenges in pricing, due to high infrastructure and computation costs, multi-dimensional and task-dependent Quality of Service (QoS), and growing concerns around liability in high-stakes applications. In this work, we propose PACT, a Pricing framework for cloud-based Agentic AI services through a Contract-Theoretic approach, which models QoS along both objective (e.g., response time) and subjective (e.g., user satisfaction) dimensions. PACT accounts for computational, infrastructure, and potential liability costs for the service provider, while ensuring incentive compatibility and individual rationality for the user under information asymmetry. Through contract-based selection, users receive tailored service offerings aligned with their needs. Numerical evaluations demonstrate that PACT improves QoS alignment between users and providers and offers a scalable, liable approach to pricing agentic AI services in the future.

PACT: A Contract-Theoretic Framework for Pricing Agentic AI Services Powered by Large Language Models

TL;DR

PACT tackles the pricing challenge for agentic AI services powered by LLMs under information asymmetry and multi-dimensional QoS. It introduces a contract-theoretic framework that models QoS with latency and user satisfaction through and incorporates liability costs to reflect regulatory risk, while guaranteeing incentive compatibility and individual rationality via a contract menu. The paper shows how to reduce IR/IC constraints using LDIC/LUIC arguments and solves the resulting optimization with a Lagrangian approach, demonstrating via simulations that users select their truthful contracts and that liability considerations influence pricing and QoS levels. This framework supports scalable, accountable pricing for cloud-based agentic AI in high-stakes domains and motivates further work on auditing and liability design to enhance safety and deployment viability.

Abstract

Agentic AI, often powered by large language models (LLMs), is becoming increasingly popular and adopted to support autonomous reasoning, decision-making, and task execution across various domains. While agentic AI holds great promise, its deployment as services for easy access raises critical challenges in pricing, due to high infrastructure and computation costs, multi-dimensional and task-dependent Quality of Service (QoS), and growing concerns around liability in high-stakes applications. In this work, we propose PACT, a Pricing framework for cloud-based Agentic AI services through a Contract-Theoretic approach, which models QoS along both objective (e.g., response time) and subjective (e.g., user satisfaction) dimensions. PACT accounts for computational, infrastructure, and potential liability costs for the service provider, while ensuring incentive compatibility and individual rationality for the user under information asymmetry. Through contract-based selection, users receive tailored service offerings aligned with their needs. Numerical evaluations demonstrate that PACT improves QoS alignment between users and providers and offers a scalable, liable approach to pricing agentic AI services in the future.

Paper Structure

This paper contains 12 sections, 5 theorems, 27 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Latency of the LLM Service
  4. User Satisfaction with the LLM Service
  5. Quality of the LLM Service
  6. Cost of the LLM Service
  7. Contract Design for Service Pricing
  8. The User's Type and Utility
  9. The Service Provider's Profit
  10. Optimal Contract
  11. Simulation Results
  12. Conclusion

Key Result

Lemma 1

For any feasible contract $\Omega(\Theta)=\{(q_k, p_k), \theta_k \in \Theta\}$, $q_k>q_j$ if and only if $\theta_k > \theta_j$, with the equality holds if and only if $\theta_k=\theta_j$.

Figures (4)

  • Figure 1: An illustration of cloud-based agentic AI services for tasks in different domains.
  • Figure 2: User utilities for types 1,5,10,15 under different contract options. The results show that each user achieves the highest utility by selecting the contract designed for their type.
  • Figure 3: The QoS levels and corresponding prices of contracts for different user types. Here, L indicates the liability cost, and (F) represents first-best results.
  • Figure 4: The user's and provider's utilities as well as the social welfare (sum of the user's and provider's utilities).

Theorems & Definitions (13)

  • Definition 1: User Types
  • Definition 2
  • Definition 3
  • Lemma 1
  • proof
  • Proposition 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • ...and 3 more