Scalable Neural Incentive Design with Parameterized Mean-Field Approximation

TL;DR

This paper introduces a scalable incentive design method for large multi-agent systems using parameterized mean-field approximation, providing theoretical guarantees and an efficient algorithm that improves revenue in auction settings.

Contribution

It formalizes incentive design as a parameterized mean-field game and develops the AMID algorithm with provable approximation bounds for large agent populations.

Findings

AMID algorithm effectively increases revenue in auction settings.

Theoretical approximation bounds hold even with discontinuous dynamics.

Scalable incentive design is feasible for large multi-agent systems.

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.