Scalable Neural Incentive Design with Parameterized Mean-Field Approximation

2025-10-24

AI Summary

Designing scalable incentive mechanisms for large-scale multi-agent systems remains challenging due to the intractability of Nash equilibrium computation and poor scalability of equilibrium-inducing methods. Method: This paper proposes a neural incentive design framework grounded in mean-field game (MFG) theory. It establishes, for the first time, a convergence rate bound of $O(1/sqrt{N})$ between finite-population incentive objectives and their mean-field approximations—even under discontinuous dynamics such as sequential auctions. The framework introduces the Adaptive Mean-Field Incentive Design (AMID) algorithm, which integrates agent exchangeability, an explicit differentiable equilibrium operator, and the adjoint method for efficient gradient computation. Results: Experiments across diverse auction settings demonstrate that the proposed method significantly increases platform revenue—outperforming both first-price auctions and state-of-the-art baselines—while ensuring theoretical rigor and scalability to massive populations.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Large-scale security measurements

Abstract

Designing incentives for a multi-agent system to induce a desirable Nash equilibrium is both a crucial and challenging problem appearing in many decision-making domains, especially for a large number of agents $N$. Under the exchangeability assumption, we formalize this incentive design (ID) problem as a parameterized mean-field game (PMFG), aiming to reduce complexity via an infinite-population limit. We first show that when dynamics and rewards are Lipschitz, the finite-$N$ ID objective is approximated by the PMFG at rate $mathscr{O}(frac{1}{sqrt{N}})$. Moreover, beyond the Lipschitz-continuous setting, we prove the same $mathscr{O}(frac{1}{sqrt{N}})$ decay for the important special case of sequential auctions, despite discontinuities in dynamics, through a tailored auction-specific analysis. Built on our novel approximation results, we further introduce our Adjoint Mean-Field Incentive Design (AMID) algorithm, which uses explicit differentiation of iterated equilibrium operators to compute gradients efficiently. By uniting approximation bounds with optimization guarantees, AMID delivers a powerful, scalable algorithmic tool for many-agent (large $N$) ID. Across diverse auction settings, the proposed AMID method substantially increases revenue over first-price formats and outperforms existing benchmark methods.

Problem

• Designing incentives for multi-agent systems to induce desirable Nash equilibria
• Reducing complexity in incentive design via parameterized mean-field approximation
• Developing scalable algorithms for large-population incentive optimization problems

Innovation

• Parameterized mean-field game for incentive design
• Adjoint algorithm with explicit equilibrium differentiation
• Scalable optimization for large multi-agent systems