Driving Supply to Marketplaces: Optimal Platform Pricing when Suppliers Share Inventory

Abstract

Marketplace platforms such as Amazon or Farfetch provide a convenient meeting point between customers and suppliers and have become an important element of e-commerce. This sales channel is particularly interesting for suppliers that sell seasonal goods under a tight time frame, because they provide expanded reach to potential customers, even though it entails lower margins. In this dyadic relationship, a supplier needs to optimize when to share inventory with the platform, and the platform needs to set the right commission structure during the season. We characterize supplier participation into the platform in a dynamic setting, and to link it to inventory levels, demand rates, time left in the season, and commission structure. This directly drives the pricing decision made by the platform. We thus provide a framework to evaluate platform pricing policies taking into account supplier responses. We use an optimal control framework with limited inventory supply and a stochastic demand process. We study the conditions under which the supplier will accept to participate and use the platform as a sales channel. We also study the optimal static and dynamic commission structure that the platform should employ. We find that it will only participate if inventory is high relative to the time left to sell the items. As a result, the platform can only offer limited supply at the beginning of the season. Given this behavior, we find that the platform and the system are always better off with dynamic pricing, while the supplier prefers static pricing. Interestingly, when the inventory decision is contingent on the platform pricing policy, the platform will often find it beneficial to commit to a static price to incentivize the supplier to stock up, highlighting that inability to commit to fixed commissions may destroy value through double marginalization effects. Our work suggests that platforms should commit to static commission structures, so as to provide the incentive for suppliers to stock up, and refrain from dynamically adjusting the commission even though these are better in the short term.