Existence of GE: Are the Cases of Non Existence a Cause of Serious Worry?

In this work, we attempt to characterize the main theoretical difficulties to prove the existence of competitive equilibrium in infinite dimensional models. We shall show cases in which it is not possible to prove the existence of equilibrium and some others in which, however the existence of equilibrium can be proved, the equilibrium prices seem not to have natural economic interpretation. Nevertheless in pure exchange economies, most of these difficulties may be avoided by mild restrictions on the model. In productive economies new specifics problem appear, for instance non convexity of the production sets or non boundedness of the feasible allocation sets. To prove the existence and the efficiency of the equilibrium in productive economies we need some strong hypothesis about the technological possibilities of each firm.

Common Mathematical Foundations of Expected Utility and Dual Utility Theories

We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous linear functionals from functional analysis. Our analysis reveals the dual character of utility functions. We also derive new integral representations of dual utility models

Linear and non-linear price decentralization

Compendious and thorough solutions to the existence of a linear price equilibrium problem, the second welfare theorem, and the limit theorem on the core are provided for exchange economies whose consomption sets are the positive cone of arbitrary ordered Fréchet-dispensing entirely with the assumption that the vector ordering of the commodity space is a lattice. The motivation comes from economic applications showing the need to bring within the scope of equilibrium theory vector orderings that are not lattices, which arise in the typical model of portfolio trading with missing options. The assumptions are on the primitives of the model. They are bounds on the marginals of non-linear prives and for omega-proper economies they are both sufficient and necessary.Linear and non-linear prices; equilibrium; welfare theorems

Approximate social nash equilibria and applications

In this paper, a concept of approximate social Nash equilibria is considered and an existence result is given when the strategic spaces of the players are not compact. These have been obtained using an approximate fixed point theorem. As an application of the existence of such approximate social Nash equilibria, sufficient conditions for the existence of a suitable approximate walrasian equilibrium in finite economies are obtained. Among others things, it is shown that the approximate walrasian equilibrium here considered is approximatively weakly efficient.Abstract economy, approximate social Nash equilibrium, finite economy, approximate walrasian equilibrium, approximate fixed point theorems.

General equilibrium analysis in ordered topological vector spaces

The second welfare theorem and the core-equivalence theorem have been proved to be fundamental tools for obtaining equilibrium existence theorems, especially in an infinite dimensional setting. For well-behaved exchange economies that we call proper economies, this paper gives (minimal) conditions for supporting with prices Pareto optimal allocations and decentralizing Edgeworth equilibrium allocations as non-trivial equilibria. As we assume neither transitivity nor monotonicity on the preferences of consumers, most of the existing equilibrium existence results are a consequence of our results. A natural application is in Finance, where our conditions lead to new equilibrium existence results, and also explain why some financial economies fail to have equilibrium.Equilibrium; Valuation equilibrium; Pareto-optimum; Edgeworth equilibrium; Properness; ordered topological vector spaces; Riesz-Kantorovich formula; sup-convolution