A game theory derivation of a classical financial equilibrium model

We consider a financial equilibrium model which deals with economic sectors and financial instruments. In the classical derivation the equilibrium prices of the financial instruments are exogenous, since the maximization of the utility functions of the sectors is performed with respect to the assets and liabilities only and, as a consequence, the associated KKT system does not yield the equilibrium prices, which are subsequently fixed with the help of an independent economic argument. Instead, we consider both the sectors and the instruments as players of a game whose Nash equilibria provide assets, liabilities and prices. We investigate the Nash equilibria using the variational inequality associated to the pseudogradient of the game. Since the pseudogradient is monotone, but not strictly monotone, we expect multiple solutions and under additional assumptions we find out a relationship between any two solutions. We then compute the solution whose price vector has minimum norm, and also study the price of anarchy of our game. At last, we perform a scenario analysis based on different taxation regimes.