A note on economic equilibrium and financial networks

Abstract

Nagurney (1999) used variational inequalities to study economic equilibrium and financial networks and applied the modified projection method to solve the problem. In this paper, we formulate the problem as a nonlinear complementarity problem. The complementarity model is just the KKT condition for the model of Nagurney (1999). It is a simpler model than that of Nagurney (1999). We also establish sufficient conditions for existence and uniqueness of the equilibrium pattern, which are weaker than those in Nagurney (1999). Finally, we apply a smoothing Newton-type algorithm to solve the problem and report some numerical results.