A Game-Theoretic Model for Product Placement in Online Platform Markets

Motivated by online platforms such as Amazon, Airbnb, etc., we consider the following Bertrand game model of product placement: a number of sellers (e.g., apartment owners) are interested in placing their products on a platform’s (e.g., Airbnb.com) website. We assume that the price of a product is determined by the the number of available sellers and their qualities, and the probability with which a platform user will buy a product is a function of the prices and the qualities, according to a multinomial logit model. In other words, the outcomes, i.e., the realized prices and sales, are determined by the Nash equilibrium of a Bertrand game. The platform can affect the outcome of the game by deciding on a mechanism to determine which products to display on their websites. For such a Bertrand game, we derive optimal mechanisms for the platform to maximize either social welfare or revenue.