Pricing with Tips in Three-Sided Delivery Platforms

TL;DR

This paper models a three-sided delivery platform incorporating tips, demonstrating how tips influence market equilibrium existence, welfare, and computational complexity, with conditions for efficient and computable equilibria.

Contribution

It introduces a model for tipping in three-sided platforms, analyzing its impact on equilibrium existence, welfare, and computational challenges, and identifies conditions for efficient solutions.

Findings

With tips, equilibrium always exists, unlike without tips.

Optimal with-tip equilibria have higher or equal welfare compared to without tips.

Efficient equilibria may not always exist; computing optimal welfare is NP-hard.

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.