Price Variation in a Bipartite Exchange Network

We analyze the variation of prices in a model of an exchange market introduced by Kakade et al. [11], in which buyers and sellers are represented by vertices of a bipartite graph and trade is allowed only between neighbors. In this model the graph is generated probabilistically, and each buyer is connected via preferential attachment to vsellers. We show that even though the tail of the degree distribution of the sellers gets heavier as vincreases, the prices at equilibrium decrease exponentially with v. This strengthens the intuition that as the number of vendors available to buyers increases, the prices of goods decrease.