Platform Equilibrium: Analayzing Social Welfare in Online Market Places

TL;DR

This paper models a market with buyers and sellers where platforms set transaction fees, analyzing how equilibrium behaviors affect social welfare, and providing algorithms and bounds for welfare approximation in various market settings.

Contribution

It introduces the concept of Platform Equilibrium, analyzes existence and welfare bounds, and extends results to multiple platforms and more complex market conditions.

Findings

Pure equilibria always exist in homogeneous-goods markets.

Platform equilibrium guarantees a logarithmic approximation of optimal welfare.

Light regulation improves welfare guarantees, with specific bounds on price of anarchy.

Abstract

We introduce the theoretical study of a Platform Equilibrium in a market with unit-demand buyers and unit-supply sellers. Each seller can join a platform and transact with any buyer or remain off-platform and transact with a subset of buyers whom she knows. Given the constraints on trade, prices form a competitive equilibrium and clears the market. The platform charges a transaction fee to all on-platform sellers, in the form of a fraction of on-platform sellers' price. The platform chooses the fraction to maximize revenue. A Platform Equilibrium is a Nash equilibrium of the game where each seller decides whether or not to join the platform, balancing the effect of a larger pool of buyers to trade with, against the imposition of a transaction fee. Our main insights are: (i) In homogeneous-goods markets, pure equilibria always exist and can be found by a polynomial-time algorithm; (ii) When the platform is unregulated, the resulting Platform Equilibrium guarantees a tight $\Theta(log(min(m, n)))$-approximation of the optimal welfare in homogeneous-goods markets, where $n$ and $m$ are the number of buyers and sellers respectively; (iii) Even light regulation helps: when the platform's fee is capped at $\alpha\in[0,1)$, the price of anarchy is 2-$\alpha$/1-$\alpha$ for general markets. For example, if the platform takes 30 percent of the seller's revenue, a rather high fee, our analysis implies the welfare in a Platform Equilibrium is still a 0.412-fraction of the optimal welfare. Our main results extend to markets with multiple platforms, beyond unit-demand buyers, as well as to sellers with production costs.