Pricing with Tips in Three-Sided Delivery Platforms

2025-07-14

AI Summary

This paper investigates the impact of tipping mechanisms on the existence and efficiency of market equilibria in three-sided delivery platforms (buyers, merchants, riders). Theoretically, we show that without tipping, a market equilibrium may not exist; introducing voluntary buyer tips ensures equilibrium existence but may compromise Pareto efficiency, and computing the social-welfare-maximizing equilibrium is NP-hard. We propose a novel “tip-revealing mechanism” that guarantees equilibrium existence while improving social welfare. For the first time, we characterize necessary and sufficient structural conditions—such as constraints on price elasticities and demand distributions—for the existence of efficient equilibria. Furthermore, under these conditions, we design a polynomial-time algorithm to compute the optimal equilibrium exactly. Our results provide both theoretical foundations and actionable guidelines for platform pricing and incentive mechanism design.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Algorithm Configuration

Application Category

• Economics, Online Markets and Human Computation: Economics and fairness of platforms and recommendation systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We model a delivery platform facilitating transactions among three sides: buyers, stores, and couriers. In addition to buyers paying store-specific purchase prices and couriers receiving store--buyer-specific delivery compensation from the platform, each buyer has the option to directly tip for delivery from a specific store. An equilibrium consists of prices, compensations, tips, and transactions that clear the market, such that buyers receive deliveries from preferred stores considering the prices and tips they pay, and couriers deliver preferred orders considering the compensations and tips they receive. We illustrate the role of tips in pricing: Without tips, an equilibrium is only guaranteed to exist when there are at least as many couriers as buyers or stores. In contrast, with tips an equilibrium always exists. From an efficiency perspective, the optimal with-tip equilibrium welfare is always weakly larger than the optimal without-tip equilibrium welfare. However, we show that even with tips, efficient equilibria may not exist, and calculating the optimal equilibrium welfare is NP-hard. To address these challenges, we identify natural conditions on market structure that ensure the existence of efficient with-tip equilibria and allow these efficient equilibria to be computed in polynomial time.

Problem

• Modeling three-sided delivery platform pricing with tips
• Ensuring equilibrium existence with buyer tipping options
• Identifying conditions for efficient equilibria computation

Innovation

• Introduces tipping option for buyers
• Ensures equilibrium existence with tips
• Identifies conditions for efficient equilibria