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Pricing Experiments in Matching Marketplaces under Interference: Designs and Estimators

Arthur Delarue, Kleanthis Karakolios

TL;DR

The paper studies interference in pricing experiments within matching marketplaces and shows that standard estimators are biased, with the bias sign depending on whether treated and untreated units are matched differently. It introduces a shadow price estimator that uses dual variables from the platform’s matching LP to reduce bias, and provides fluid-limit proofs and finite-sample validation. The work analyzes two designs (cost-excluded and cost-included) and demonstrates that shadow-price corrections improve inference under both, with practical guidance favoring indistinguishable matching to minimize interference. These insights offer principled design choices for platform experiments and robust methods to quantify global treatment effects when pricing interventions interact with matching. The findings have direct implications for ride-hailing and other marketplace platforms where pricing and matching decisions intertwine and interference is inevitable.

Abstract

Interference between treated and untreated units is a source of bias in marketplace experiments. In this paper, we specifically consider pricing interventions, in which a platform seeks to adjust base pricing levels at the marketplace level in order to increase demand. In a matching marketplace, this type of experiment leads to a crucial design question: should the platform match treated and untreated units differently because they paid different prices? We find that standard estimation techniques are biased, but the sign of this bias depends strongly on this design choice. Bias can be reduced by using the ``shadow price estimator'', which relies on the optimal dual solution of the platform's supply-demand matching problem -- especially when the platform chooses to ignore pricing differences at matching time. We validate our findings both theoretically in a fluid limit setting, and numerically in a finite-sample setting.

Pricing Experiments in Matching Marketplaces under Interference: Designs and Estimators

TL;DR

The paper studies interference in pricing experiments within matching marketplaces and shows that standard estimators are biased, with the bias sign depending on whether treated and untreated units are matched differently. It introduces a shadow price estimator that uses dual variables from the platform’s matching LP to reduce bias, and provides fluid-limit proofs and finite-sample validation. The work analyzes two designs (cost-excluded and cost-included) and demonstrates that shadow-price corrections improve inference under both, with practical guidance favoring indistinguishable matching to minimize interference. These insights offer principled design choices for platform experiments and robust methods to quantify global treatment effects when pricing interventions interact with matching. The findings have direct implications for ride-hailing and other marketplace platforms where pricing and matching decisions intertwine and interference is inevitable.

Abstract

Interference between treated and untreated units is a source of bias in marketplace experiments. In this paper, we specifically consider pricing interventions, in which a platform seeks to adjust base pricing levels at the marketplace level in order to increase demand. In a matching marketplace, this type of experiment leads to a crucial design question: should the platform match treated and untreated units differently because they paid different prices? We find that standard estimation techniques are biased, but the sign of this bias depends strongly on this design choice. Bias can be reduced by using the ``shadow price estimator'', which relies on the optimal dual solution of the platform's supply-demand matching problem -- especially when the platform chooses to ignore pricing differences at matching time. We validate our findings both theoretically in a fluid limit setting, and numerically in a finite-sample setting.

Paper Structure

This paper contains 31 sections, 19 theorems, 110 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Model Description
  4. Supply and Demand Arrival Processes
  5. Matching Mechanism
  6. Estimating Treatment Effects
  7. Global treatment effect.
  8. Experimental data.
  9. Matching Fluid Limit
  10. Dependence of Interference Bias on the Experimental Design
  11. Cost-Excluded Design
  12. Cost-Included Design
  13. Bias Reduction Via Shadow Prices
  14. Cost-Excluded Design
  15. Cost-Included Design
  16. ...and 16 more sections

Key Result

Lemma 1

Under both cost models, for any allowed values of $\kappa$ or $\alpha$, the optimal matching is obtained by solving $\Phi_{\text{CE}}(\cdot)$, ignoring all treatment costs.

Figures (13)

  • Figure 1: Motivating example: matching with one demand type.
  • Figure 2: Bias of the cost-excluded RCT estimator.
  • Figure 3: Bias of the RCT-CI estimator on the simple example from Figure \ref{['fig:setup']}.
  • Figure 4: Bias of the cost-excluded shadow price estimator.
  • Figure 5: Bias of the SP-CI estimator on the simple example from Figure \ref{['fig:setup']}.
  • ...and 8 more figures

Theorems & Definitions (26)

  • Lemma 1
  • Definition 1
  • Remark 1
  • Lemma 2
  • Proposition 1: Fluid limit of matching problems
  • Corollary 1
  • Definition 2
  • Lemma 3
  • Theorem 1
  • Definition 3
  • ...and 16 more