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Microeconomic Foundations of Multi-Agent Learning

Nassim Helou

TL;DR

The paper develops a formal framework for incentive-aware learning in dynamic principal–agent environments, where both the principal and the agent learn within a Markov decision process and externalities couple their outcomes. It introduces a two-phase mechanism: Phase 1 estimates implementable transfers that align the agent’s actions with welfare, and Phase 2 uses these estimates to steer long-run dynamics via a shifted, welfare-maximizing objective, achieving sublinear social-welfare regret under mild regularity and exploration conditions. A central theoretical result shows that, with appropriate choice of exponents, the principal can guarantee $R_{sw}(T)=o(T)$, i.e., asymptotically optimal welfare. Beyond learning, the work links diffusion models to economic aggregation, showing the diffusion denoiser corresponds to the welfare-maximizing aggregator in a social planner and equilibrium in a large economy, providing a principled interpretation of diffusion models as welfare-maximizing mechanisms. Simulations illustrate how simple subsidies can substantially improve welfare in stateful externality settings, underscoring the practical relevance for safe and welfare-aligned AI in markets and insurance.

Abstract

Modern AI systems increasingly operate inside markets and institutions where data, behavior, and incentives are endogenous. This paper develops an economic foundation for multi-agent learning by studying a principal-agent interaction in a Markov decision process with strategic externalities, where both the principal and the agent learn over time. We propose a two-phase incentive mechanism that first estimates implementable transfers and then uses them to steer long-run dynamics; under mild regret-based rationality and exploration conditions, the mechanism achieves sublinear social-welfare regret and thus asymptotically optimal welfare. Simulations illustrate how even coarse incentives can correct inefficient learning under stateful externalities, highlighting the necessity of incentive-aware design for safe and welfare-aligned AI in markets and insurance.

Microeconomic Foundations of Multi-Agent Learning

TL;DR

The paper develops a formal framework for incentive-aware learning in dynamic principal–agent environments, where both the principal and the agent learn within a Markov decision process and externalities couple their outcomes. It introduces a two-phase mechanism: Phase 1 estimates implementable transfers that align the agent’s actions with welfare, and Phase 2 uses these estimates to steer long-run dynamics via a shifted, welfare-maximizing objective, achieving sublinear social-welfare regret under mild regularity and exploration conditions. A central theoretical result shows that, with appropriate choice of exponents, the principal can guarantee , i.e., asymptotically optimal welfare. Beyond learning, the work links diffusion models to economic aggregation, showing the diffusion denoiser corresponds to the welfare-maximizing aggregator in a social planner and equilibrium in a large economy, providing a principled interpretation of diffusion models as welfare-maximizing mechanisms. Simulations illustrate how simple subsidies can substantially improve welfare in stateful externality settings, underscoring the practical relevance for safe and welfare-aligned AI in markets and insurance.

Abstract

Modern AI systems increasingly operate inside markets and institutions where data, behavior, and incentives are endogenous. This paper develops an economic foundation for multi-agent learning by studying a principal-agent interaction in a Markov decision process with strategic externalities, where both the principal and the agent learn over time. We propose a two-phase incentive mechanism that first estimates implementable transfers and then uses them to steer long-run dynamics; under mild regret-based rationality and exploration conditions, the mechanism achieves sublinear social-welfare regret and thus asymptotically optimal welfare. Simulations illustrate how even coarse incentives can correct inefficient learning under stateful externalities, highlighting the necessity of incentive-aware design for safe and welfare-aligned AI in markets and insurance.
Paper Structure (23 sections, 4 theorems, 36 equations, 1 figure)

This paper contains 23 sections, 4 theorems, 36 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Related Work
  3. Incentive Design in a Principal Agent MDPs with Externalities
  4. Setting
  5. Policies and Social Welfare.
  6. Players' Behaviors
  7. Agent Learning and Rationality.
  8. Principal’s Objective and Welfare Regret.
  9. Principal’s Two-Phase Algorithm
  10. Phase 1: Transfer Estimation.
  11. Phase 2: Welfare Optimization.
  12. Main Result
  13. Diffusion Models as Welfare Maximizing Economic Mechanisms
  14. Diffusion Preliminaries
  15. A Social Planner Problem
  16. ...and 8 more sections

Key Result

Theorem 1

Assume the agent satisfies hindsight rationality with exponent $\kappa < 1$ and that the MDP is uniformly ergodic under exploratory policies, ensuring that each state is visited $\Theta(T^\alpha)$ times per batch for some $\alpha>0$. Suppose the principal chooses exponents $\alpha,\beta \in (0,1)$ s Then there exists a two-phase principal’s algorithm such that with high probability: where $\gamma

Figures (1)

  • Figure 1: Effect of incentives in a principal–agent MDP with a stateful externality. Above: rolling average social welfare. Below: rolling average terminal pollution. Introducing a simple subsidy significantly improves welfare by inducing pollution abatement.

Theorems & Definitions (7)

  • Definition 1: Agent Rationality
  • Theorem 1: Social Efficiency in Principal--Agent MDPs
  • Proposition 1: Bayesian Denoiser Maximizes Welfare
  • proof
  • Corollary 1: Diffusion Training = Welfare Maximization
  • proof
  • Proposition 2: Diffusion Drift as Welfare-Maximizing Equilibrium