Deep Incentive Design with Differentiable Equilibrium Blocks

TL;DR

This work proposes 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.

Abstract

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).

Figures (7)

• Figure 1: Deep Incentive Design framework. Black (green) arrows show the forward (backward) computation.
• Figure 2: A simple example of a contract design problem with action space $2{\times}2$ and 3 outcomes.
• Figure 3: $\sigma^\omega$ is plotted in cyan, the $0.01$-ME-CCE in magenta. The red polytope corresponds to the $0.01$-CCE set. The underlying game is between a row player with actions Up and Down and a column player with actions Left and Right. The four vertices represent the four deterministic joint actions. Figure was produced with a smaller network trained on $2{\times}2$ games.
• Figure 4: Inverse equilibrium training pipeline.
• Figure 5: The architecture of the contract design mechanism generator. Blue boxes show the core generator and the green text shows the shapes.