{"ID":2850654,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.21442","arxiv_id":"2510.21442","title":"Scalable Neural Incentive Design with Parameterized Mean-Field Approximation","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.","short_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...","url_abs":"https://arxiv.org/abs/2510.21442","url_pdf":"https://arxiv.org/pdf/2510.21442v1","authors":"[\"Nathan Corecco\",\"Batuhan Yardim\",\"Vinzenz Thoma\",\"Zebang Shen\",\"Niao He\"]","published":"2025-10-24T13:18:54Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"cs.LG\",\"cs.MA\"]","methods":"[]","has_code":false}