Nash and Wardrop equilibria in aggregative games with coupling constraints

We consider the framework of aggregative games, in which the cost function of each agent depends on his own strategy and on the average population strategy. As first contribution, we investigate the relations between the concepts of Nash and Wardrop equilibrium. By exploiting a characterization of the two equilibria as solutions of variational inequalities, we bound their distance with a decreasing function of the population size. As second contribution, we propose two decentralized algorithms that converge to such equilibria and are capable of coping with constraints coupling the strategies of different agents. Finally, we study the applications of charging of electric vehicles and of route choice on a road network.Comment: IEEE Trans. on Automatic Control (Accepted without changes). The first three authors contributed equall

Merit functions: a bridge between optimization and equilibria

In the last decades, many problems involving equilibria, arising from engineering, physics and economics, have been formulated as variational mathematical models. In turn, these models can be reformulated as optimization problems through merit functions. This paper aims at reviewing the literature about merit functions for variational inequalities, quasi-variational inequalities and abstract equilibrium problems. Smoothness and convexity properties of merit functions and solution methods based on them will be presented

Existence and solution methods for equilibria

Equilibrium problems provide a mathematical framework which includes optimization, variational inequalities, fixed-point and saddle point problems, and noncooperative games as particular cases. This general format received an increasing interest in the last decade mainly because many theoretical and algorithmic results developed for one of these models can be often extended to the others through the unifying language provided by this common format. This survey paper aims at covering the main results concerning the existence of equilibria and the solution methods for finding them

Existence for Competitive Equilibrium by Means of Generalized Quasivariational Inequalities

A competitive economic equilibrium model integrated with exchange, consumption, and production is considered. Our goal is to give an existence result when the utility functions are concave, proper, and upper semicontinuous. To this aim we are able to characterize the equilibrium by means of a suitable generalized quasi-variational inequality; then we give the existence of equilibrium by using the variational approach

THE RHETORIC OF DUALITY

Agricultural economistsÂ’' view of duality has often assumed the characteristics of an ambivalent relation. During the eighties, several authors published papers which put in doubt this or that aspects of duality. This study emphasizes the notion that duality is a time-honored approach suitable for solving problems that can be expressed mathematically. Contrary to many assertions that appeared in the agricultural economics literature, duality does not seem to suffer from any theoretical limitations any more than does the formulation of the primal problem. The article presents two problems that can be solved with dual methods. The authors are incapable of deriving the same results using primal approach.Research Methods/ Statistical Methods,