Bertrand Duopoly in Online Consumer-to-Consumer Markets

In this note I examine price competition between two sellers who sequentially arrive to an online consumer-to-consumer market (e.g., Craigslist). Each seller has one unit of a homogeneous good that they want to sell to a pool of buyers. When buyers arrive randomly to the market, I show that there is a unique equilibrium, in which sellers choose different prices and earn the same profit. When buyers' arrival positively correlates with their valuations, an additional equilibrium outcome has sellers choose almost the same prices but with the second-arriving seller earning a higher profit. I discuss how these results relate to the environment of traditional markets analyzed in Hviid (1990)