# Differentiable Economics for Randomized Affine Maximizer Auctions

Source: [Differentiable Economics for Randomized Affine Maximizer Auctions](<https://www.sota2.com/research/paper/68fa6bc21e209131cea301fb>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T23:56:05.140Z

Authors: Michael Curry, Tuomas Sandholm, John Dickerson

Published: 2022-02-06T22:01:21.000Z

## Abstract

A recent approach to automated mechanism design, differentiable economics, represents auctions by rich function approximators and optimizes their performance by gradient descent. The ideal auction architecture for differentiable economics would be perfectly strategyproof, support multiple bidders and items, and be rich enough to represent the optimal (i.e. revenue-maximizing) mechanism. So far, such an architecture does not exist. There are single-bidder approaches (MenuNet, RochetNet) which are always strategyproof and can represent optimal mechanisms. RegretNet is multi-bidder and can approximate any mechanism, but is only approximately strategyproof. We present an architecture that supports multiple bidders and is perfectly strategyproof, but cannot necessarily represent the optimal mechanism. This architecture is the classic affine maximizer auction (AMA), modified to offer lotteries. By using the gradient-based optimization tools of differentiable economics, we can now train lottery AMAs, competing with or outperforming prior approaches in revenue.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Auction Revenue Maximization on Classic auction Setting (E) 1x2](<https://www.sota2.com/research/sota/auction-revenue-maximization-on-classic-auction-setting-e-1x2.md>): Auction Revenue Maximization; Classic auction Setting (E) 1x2; Avg Revenue: 9.3139.

- [Auction Revenue Maximization on Classic auction Setting (F) 1x2](<https://www.sota2.com/research/sota/auction-revenue-maximization-on-classic-auction-setting-f-1x2.md>): Auction Revenue Maximization; Classic auction Setting (F) 1x2; Average Revenue: 15.44.

- [Auction Revenue Maximization on Classic auction Setting (D) 3x1](<https://www.sota2.com/research/sota/auction-revenue-maximization-on-classic-auction-setting-d-3x1.md>): Auction Revenue Maximization; Classic auction Setting (D) 3x1; Average Revenue: 2.7238.

- [Auction Revenue Maximization on Classic auction Setting (C) 5x5](<https://www.sota2.com/research/sota/auction-revenue-maximization-on-classic-auction-setting-c-5x5.md>): Auction Revenue Maximization; Classic auction Setting (C) 5x5; Avg Revenue: 2.8527.

- [Optimal Auction Design on 2x5 auction setting](<https://www.sota2.com/research/sota/optimal-auction-design-on-2x5-auction-setting.md>): Optimal Auction Design; 2x5 auction setting; Revenue: 2.2354.

- [Optimal Auction Design on 3x10 auction setting](<https://www.sota2.com/research/sota/optimal-auction-design-on-3x10-auction-setting.md>): Optimal Auction Design; 3x10 auction setting; Revenue: 5.345.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2202.02872>)

[PDF](<https://arxiv.org/pdf/2202.02872.pdf>)