Scalable Neural Incentive Design with Parameterized Mean-Field Approximation
Nathan Corecco, Batuhan Yardim, Vinzenz Thoma, Zebang Shen, Niao He
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 large numbers 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 $\mathcal{O}(\frac{1}{\sqrt{N}})$.Moreover, beyond the Lipschitz-continuous setting, we prove the same $\mathcal{O}(\frac{1}{\sqrt{N}})$ 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 large-$N$ ID.Across diverse auction settings, the proposed AMID method substantially increases revenue over first-price formats and outperforms existing benchmark methods.