The existence of an equilibrium in an extended Walrasian economic model of exchange is confirmed constructively, under broad assumptions , by an iterative process. In this process, truncated variational inequality problems are solved in which the agents' budget constraints are furnished with a penalty representation. Epi-convergence arguments are used to… (More)
We establish, in innnite dimensional Banach space, a nonconvex separation property for general closed sets that is an extension of Hahn-Banach separation theorem. We provide some consequences in optimization, in particular the existence of singular multipliers and show the relation of our principle with the extremal principle of Mordukhovich.
We explore convergence notions for bivariate functions that yield convergence and stability results for their maxinf (or minsup) points. This lays the foundations for the study of the stability of solutions to variational inequalities, the solutions of inclusions, of Nash equilibrium points of non-cooperative games and Walras economic equilibrium points, of… (More)
In the prevailing theory of economic equilibrium with incomplete markets, assets pay in " units of account " which are regarded as money but have no link to the actual currencies that rule in financial dealings. The units of account at any given time are unrelated to those at another time or in another state, as if the money in question must be disposed of… (More)
It's shown that a number of variational problems can be cast as finding the maxinf-points (or minsup-points) of bivariate functions, coveniently abbreviated to bifunctions. These variational problems include: linear and nonlinear complementarity problems, fixed points, variational inequalities, inclusions, non-cooperative games, Walras and Nash equilibrium… (More)
In an economic model of exchange of goods, the preference structure can be specified by utility functions. Under utility conditions identified here more broadly than usual, except for concavity in place of quasi-concavity, every equilibrium will be stable in a doubly local sense with respect to shifts in the agent's holdings and Walrasian tâtonnement. This… (More)
—We extend the traditional two-stage linear stochastic program by probabilistic constraints imposed in the second stage. This adds nonlinear-ity such that basic arguments for analyzing the structure of linear two-stage stochastic programs have to be rethought from the very beginning. We identify assumptions under which the problem is structurally sound and… (More)
In the models of multi-stage equilibrium with uncertain financial markets that have so far been formulated in extension of the classical Walrasian model with only a single stage, each state is completely isolated in its activity. If there is production, it ends in the state in which it begins. Goods that are not consumed within a state merely perish.… (More)