# Deep Incentive Design with Differentiable Equilibrium Blocks

arXiv: https://arxiv.org/abs/2603.07705 · HTML: https://mlsanity.com/paper/2603.07705/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 84 references that are in the map.
- First posted on arXiv 8 Mar 2026.

## Builds on (most cited first, 30 of 46)

- [RouteLLM: Learning to Route LLMs with Preference Data](https://mlsanity.com/paper/2406.18665/) (2024)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [RouterBench: A Benchmark for Multi-LLM Routing System](https://mlsanity.com/paper/2403.12031/) (2024)
- [Nash Learning from Human Feedback](https://mlsanity.com/paper/2312.00886/) (2023)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [V-Learning -- A Simple, Efficient, Decentralized Algorithm for Multiagent RL](https://mlsanity.com/paper/2110.14555/) (2021)
- [Near-Optimal Reinforcement Learning with Self-Play](https://mlsanity.com/paper/2006.12007/) (2020)
- [Universal Model Routing for Efficient LLM Inference](https://mlsanity.com/paper/2502.08773/) (2025)
- [Aligning Superhuman AI with Human Behavior: Chess as a Model System](https://mlsanity.com/paper/2006.01855/) (2020)
- [Modeling Strong and Human-Like Gameplay with KL-Regularized Search](https://mlsanity.com/paper/2112.07544/) (2021)
- [Mastering the Game of No-Press Diplomacy via Human-Regularized Reinforcement Learning and Planning](https://mlsanity.com/paper/2210.05492/) (2022)
- [Principled Penalty-based Methods for Bilevel Reinforcement Learning and RLHF](https://mlsanity.com/paper/2402.06886/) (2024)
- [PARL: A Unified Framework for Policy Alignment in Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2308.02585/) (2023)
- [Optimal Auctions through Deep Learning: Advances in Differentiable Economics](https://mlsanity.com/paper/1706.03459/) (2017)
- [Complexity of Mechanism Design](https://mlsanity.com/paper/1408.1486/) (2014)
- [Auction learning as a two-player game](https://mlsanity.com/paper/2006.05684/) (2020)
- [Optimal-er Auctions through Attention](https://mlsanity.com/paper/2202.13110/) (2022)
- [Computational Rationalization: The Inverse Equilibrium Problem](https://mlsanity.com/paper/1308.3506/) (2013)
- [A Scalable Neural Network for DSIC Affine Maximizer Auction Design](https://mlsanity.com/paper/2305.12162/) (2023)
- [What game are we playing? End-to-end learning in normal and extensive form games](https://mlsanity.com/paper/1805.02777/) (2018)
- [End-to-End Learning and Intervention in Games](https://mlsanity.com/paper/2010.13834/) (2020)
- [A Context-Integrated Transformer-Based Neural Network for Auction Design](https://mlsanity.com/paper/2201.12489/) (2022)
- [Multi-Agent Contracts](https://mlsanity.com/paper/2211.05434/) (2022)
- [Contextual Bilevel Reinforcement Learning for Incentive Alignment](https://mlsanity.com/paper/2406.01575/) (2024)
- [Coordinating Followers to Reach Better Equilibria: End-to-End Gradient Descent for Stackelberg Games](https://mlsanity.com/paper/2106.03278/) (2021)
- [The Good Shepherd: An Oracle Agent for Mechanism Design](https://mlsanity.com/paper/2202.10135/) (2022)
- [Turbocharging Solution Concepts: Solving NEs, CEs and CCEs with Neural Equilibrium Solvers](https://mlsanity.com/paper/2210.09257/) (2022)
- [Adaptive Mechanism Design: Learning to Promote Cooperation](https://mlsanity.com/paper/1806.04067/) (2018)
- [Disciplined Geometric Programming](https://mlsanity.com/paper/1812.04074/) (2018)
- [Inducing Equilibria via Incentives: Simultaneous Design-and-Play Ensures Global Convergence](https://mlsanity.com/paper/2110.01212/) (2021)

## Built on by (most cited first, 2 of 2)

- [Optimal Coarse Correlated Equilibria in Mean Field Games: Linear Programming and No-Regret Learning](https://mlsanity.com/paper/2606.20062/) (2026)
- [Who Bears the Burden? Learning Responsibility for Shared Constraints in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2610.07491/) (2026)

## Abstract (arXiv)

Automated design of multi-agent interactions with desirable equilibrium outcomes is inherently difficult due to the computational hardness, non-uniqueness, and instability of the resulting equilibria. In this work, we propose the use of game-agnostic differentiable equilibrium blocks (DEBs) as modules in a novel, differentiable framework to address a wide variety of incentive design problems from economics and computer science. We call this framework deep incentive design (DID). To validate our approach, we examine three diverse, challenging incentive design tasks: contract design, machine scheduling, and inverse equilibrium problems. For each task, we train a single neural network using a unified pipeline and DEB. This architecture solves the full distribution of problem instances, parameterized by a context, handling all games across a wide range of scales (from two to sixteen actions per player).