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Scalable Neural Incentive Design with Parameterized Mean-Field Approximation
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Formalizes large-N incentive design as parameterized mean-field games, proves O(1/sqrt(N)) approximation for Lipschitz PMFGs and sequential batched auctions, and proposes AMID, an adjoint method for differentiating through iterated mean-field equilibria to optimize revenue.
Problem
Incentive design for many-agent games: choosing a parameter (e.g., auction rules or congestion prices) that induces a desirable Nash equilibrium is computationally intractable when the number of agents N is large, and existing mean-field approximations do not guarantee that the design objective is p
Approach
Model the N-player incentive design problem as a parameterized mean-field game, prove O(1/sqrt(N)) approximation of exploitability and design objective under Lipschitz continuity and also for batched auctions via no-zero-dominance policies, and compute gradients of the equilibrium-constrained objective with an adjoint (reverse-mode) scheme over iterated mirror-descent equilibrium operators with O(
Key results
- AMID reduces memory for single backpropagation at H=25 from 16960 MiB (naive) to 826 MiB (AMID) on a single H100.
- Actual finite-N revenue in the N-player auction is reported to be very close to the optimized mean-field objective even for N around 100.
- AMID substantially increases revenue over first-price formats and outperforms zeroth-order baselines (0-Adam, 0-SGD, Anneal) across settings A1-A3.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use AMID instead of naive backpropagation | A1, H=5 · A1, H=5 | time (s): $0.19 \pm 0.02$ s -> $0.09 \pm 0.01$ s | Helped |
| Use AMID instead of naive backpropagation | A1, H=10 · A1, H=10 | time (s): $0.25 \pm 0.10$ s -> $0.21 \pm 0.08$ s | Helped |
| Use AMID instead of naive backpropagation | A1, H=25 · A1, H=25 | time (s): $0.71 \pm 0.15$ s -> $0.67 \pm 0.12$ s | Helped |
| Use AMID instead of naive backpropagation | A1, H=5 · A1, H=5 | memory (MiB): 2760 MiB -> 560 MiB | Helped |
| Use AMID instead of naive backpropagation | A1, H=10 · A1, H=10 | memory (MiB): 8746 MiB -> 586 MiB | Helped |
| Use AMID instead of naive backpropagation | A1, H=25 · A1, H=25 | memory (MiB): 16960 MiB -> 826 MiB | Helped |
Limitations
- Auction approximation bound holds for policies satisfying no-zero-dominance, which true MF-NE may not satisfy; entropy-regularized equilibria are used instead.
- Worst-case bounds grow exponentially in horizon H in general.
- Gradient estimates rely on convergence of mirror descent iterates to equilibrium and spectral radius conditions.
Experimental setup
Benchmarks: beach bar MFG batched auction settings A1-A3
Metrics: revenue exploitability objective value compute time and memory
Baselines: FirstPrice 0-Adam 0-SGD Anneal
Builds on: mean-field game approximation of finite-player Nash equilibria online mirror descent for MFG equilibria adjoint method Adam
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