Dynamics of price formation on complex networks.

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Networks mediate our economic interactions. From spatial networks representing transportation routes, to more abstract networks of similarity among products, we interact, trade, and compete over networks with a complex structure. Nevertheless, classical economic models of how prices are formed under competition, such as the Edgeworth and the Hotelling models, completely neglect the network structure of real markets. Here, we introduce a dynamical model of price formation, where sellers and buyers are placed on the nodes of a network with any arbitrarily complex topology. Buyers are modeled as random walkers with perfect or limited information about the market, and their distribution depends on the prices and positions of sellers. Concurrently, sellers dynamically adjust their prices to maximize their payoff, based on the current distribution of buyers. These two dynamical processes coevolve and we show that, depending on the positions of the sellers and on the level of information available to the buyers, the model can either converge to fixed prices, or produce cycles of different amplitudes and periods, similar to those observed in real-world markets. By unveiling how competition depends dynamically on the structure of a market, our model allows to quantify the strength of competition in real-world markets and also to identify the most profitable locations for a seller. We use urban street patterns of different cities from all over the world, as examples of spatial networks, to illustrate a novel measure of node centrality, which ranks nodes based on the payoff earned by a seller placed on that node.