Equilibrium Prices on a Financial Graph

The analysis of financial markets usually assumes that trades are centralized and open to all investors. Investors are typically price takers. A relatively recent interest has been devoted to local markets open to a limited number of traders. Such markets may be fruitfully analyzed by means of graphs where traders are the nodes and trades are the arcs. In this model one bilateral trade occurs each round. Agents are risk averse and act myopically seeking to maximize their expected utility. Conditions for the agents to trade and to find an equilibrium price are determined theoretically. An ad-hoc algorithm is applied to find a numerical solution and to simulate the path towards the equilibrium price depending on different initial settings.