This paper develops an equilibrium model of decentralized markets which accommodates any structure of coexisting exchanges, including general networks and common market structures which cannot be represented by graphs. The model allows for any number of strategic traders and multiple divisible assets. We characterize equilibrium and welfare and develop comparative statics with respect to preferences, assets and market structures represented by hypergraphs. Changes in market structure that increase price impact may increase welfare. Asset substitutability and complementarity is not determined by the primitive payoff covariance but is endogenous and may differ across agents, depending on their participation in the exchanges. Less connected agents may have larger price impact and attain higher utility.