Equilibrium pricing with positive externalities

Abstract

We study the problem of selling an item to strategic buyers in the presence of positive historical externalities, where the value of a product increases as more people buy and use it. This increase in the value of the product is the result of resolving bugs or security holes after more usage. We consider a continuum of buyers that are partitioned into types where each type has a valuation function based on the actions of other buyers. Given a fixed sequence of prices, or price trajectory, buyers choose a day on which to purchase the product, i.e. they have to decide whether to purchase the product early in the game or later after more people already own it. We model this strategic setting as a game, study existence and uniqueness of the equilibria, and design an FPTAS to compute an approximately revenue-maximizing pricing trajectory for the seller in two special cases: the symmetric settings in which there is just a single buyer type, and the linear settings that are characterized by an initial type-independent bias and a linear type-dependent influenceability coefficient.