When A Platform Competes with Third-Party Sellers in Networked Markets: A Revenue Management Perspective

Abstract

We consider a platform marketplace with both third-party and first-party sellers. The platform charges commissions to third-party sellers and buyers for transactions in the marketplace. Meanwhile, it also directly determines transaction prices for first-party sellers in their sales to buyers. Sellers and buyers are divided into different types with the compatibility captured by a bipartite network. Different types of sellers and buyers are heterogeneous in their cost and utility functions. Given the platform's decisions on prices and commissions, buyers/third-party sellers maximize their own payoffs from demanding/supplying products, and market-clearing conditions are satisfied in the networked market. Facing the complexity with non-convex equilibrium constraints in the networked market, we develop a convex optimization formulation for the platform's profit-optimal price-commission vector. Moreover, we characterize how the platform's profit-optimal price-commission decision depends on the network structure featured by complement and substitution of agents' trading relation in the marketplace. We also establish the impact of network structure on the equilibrium trading quantities in the platform's profit-optimal equilibrium implementation. Besides this, under fairness consideration between the platform and its market participants, we develop an efficient (1-epsilon)-approximation algorithm to obtain a price-commission profile under which a fair allocation of surplus between the platform and its market participants is guaranteed in the equilibrium trades. Lastly, we shed light on how the platform should optimally introduce additional first-party sellers into the networked market.

Keywords: Revenue Management, Two-sided Market