Abstract:

We introduce a graph-theoretic generalization of classical Arrow-Debreu economics, in which an undirected graph specifies which consumers or economies are permitted to engage in direct trade, and the graph topology may give rise to local variations in the prices of commodities. Our main technical contributions are: (1) a general existence theorem for graphical equilibria, which require local markets to clear; (2) an improved algorithm for computing approximate equilibria in standard (non-graphical) economies, which generalizes the algorithm of Deng et al. [2002] to non-linear utility functions; (3) an algorithm for computing equilibria in the graphical setting, which runs in time polynomial in the number of consumers in the special but important case in which the graph is a tree (again permitting non-linear utility functions). We also highlight many interesting learning problems that arise in our model, and relate them to learning in standard game theory and economics, graphical games, and graphical models for probabilistic inference.

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