# Experimenting in Equilibrium

## TL;DR

This paper introduces a mean-field based experimental design method for large-scale stochastic systems with significant cross-unit interference, enabling accurate effect estimation and system optimization in equilibrium.

## Contribution

It presents a novel approach combining randomization and lightweight mean-field modeling to estimate effects and optimize parameters in systems with interference.

## Key findings

- Effective estimation of small parameter changes in large systems.
- Enables gradient-based optimization in equilibrium settings.
- Applicable to platforms optimizing supply-side incentives.

## Abstract

Classical approaches to experimental design assume that intervening on one unit does not affect other units. There are many important settings, however, where this non-interference assumption does not hold, as when running experiments on supply-side incentives on a ride-sharing platform or subsidies in an energy marketplace. In this paper, we introduce a new approach to experimental design in large-scale stochastic systems with considerable cross-unit interference, under an assumption that the interference is structured enough that it can be captured via mean-field modeling. Our approach enables us to accurately estimate the effect of small changes to system parameters by combining unobstrusive randomization with lightweight modeling, all while remaining in equilibrium. We can then use these estimates to optimize the system by gradient descent. Concretely, we focus on the problem of a platform that seeks to optimize supply-side payments p in a centralized marketplace where different suppliers interact via their effects on the overall supply-demand equilibrium, and show that our approach enables the platform to optimize p in large systems using vanishingly small perturbations.