Bertrand Duopoly in Online Consumer-to-Consumer Markets

In this paper I examine price competition between two sellers who sequentially arrive at an online consumer-to-consumer market: e.g., Craigslist. Each seller has one unit of a homogeneous good that she wants to sell to a pool of buyers. When buyers arrive randomly at 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).