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We study a simple exchange model in which price is fixed and the amount of agood transferred between actors depends only on the actors' respective budgetsand the existence of a link between transacting actors. The model induces asimply-connected but possibly multi-component bipartite graph. A tradingsession on a fixed graph consists of a sequence of exchanges between connectedbuyers and sellers until no more exchanges are possible. We deem a tradingsession "feasible" if all of the buyers satisfy their respective demands. Ifall trading sessions are feasible the graph is deemed "successful", otherwisethe feasibility of a trading session depends on the order of the sequence ofexchanges. We demonstrate that topology is important for the success of tradingsessions on graphs. In particular, for the case that supply equals demand foreach component of the graph, we prove that the graph is successful if and onlyif the graph consists of components each of which are complete bipartite. Forthe case that supply exceeds demand, we prove that the other topologies alsocan be made successful but with finite reserve (i.e., excess supply)requirements that may grow proportional to the number of buyers. Finally, withcomputations for a small instance of the model, we provide an example of thewide range of performance in which only the connectivity varies. These resultstaken together place limits on the improvements in performance that can beexpected from proposals to increase the connectivity of sparse exchangenetworks.

Sensitivity of the Performance of a Simple Exchange Model to its Topology