Variational Inequalities and General Equilibrium Models

We deal with the study of several general equilibrium models by using the variational inequality theory. The theory of variational inequalities was introduced in the sixties of the past century by Fichera (1964) [27], and Lions and Stampacchia (1965) [28], as an innovative and effective method to solve equilibrium problems arising in mathematical physics. Afterward this theory turned out as a powerful tool, and it was used to analyze different kinds of equilibrium problems. We mention the equilibrium problems of the oligopoly, of the market, of the traffic, of Nash, see, e.g., [9, 12, 26, 29]. Here is the content of this chapter. We first introduce some general equilibrium economic models; then, after recalling some basic notions on variational inequality theory, we make use of such a tool to analyze some proposed models. We consider the exchange economy model, subsequently we study the models with nominal and numeraire assets, and, finally, we consider the case of restricted participation.