Deep Incentive Design with Differentiable Equilibrium Blocks

Google DeepMind, † Research conducted during an internship at Google DeepMind. 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). Recently, Marris et al. (2022) and Liu et al. (2024) presented two distinct approaches to train neural networks to map a wide spectrum of normal-form games to their unique maximum