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.

[1]  J. Aubin.  Mathematical methods of game and economic theory , 1979 .

[2]  Frank Riedel,et al.  Existence and structure of stochastic equilibria with intertemporal substitution , 2001, Finance Stochastics.

[3]  A. Peressini.  Ordered topological vector spaces , 1967 .

[4]  Monique Florenzano,et al.  Edgeworth equilibria, fuzzy core, and equilibria of a production economy without ordered preferences , 1990 .

[5]  Nicholas C. Yannelis,et al.  A Theory of Value with Non-linear Prices: Equilibrium Analysis beyond Vector Lattices , 2001, J. Econ. Theory.

[6]  T. Andô,et al.  On fundamental properties of a Banach space with a cone , 1962 .

[7]  丸山 徹.  Convex Analysisの二,三の進展について , 1977 .

[8]  Charalambos D. Aliprantis,et al.  GENERAL EQUILIBRIUM IN INFINITE SECURITY MARKETS , 2002 .

[9]  Nicholas C. Yannelis,et al.  The Riesz-Kantorovich formula and general equilibrium theory , 2000 .

[10]  C. Aliprantis,et al.  Existence and Optimality of Competitive Equilibria , 1989 .

[11]  Herbert E. Scarf,et al.  A LIMIT THEOREM ON THE CORE OF AN ECONOMY , 1963, Classics in Game Theory.

[12]  Charalambos D. Aliprantis,et al.  Non-marketed options, non-existence of equilibria, and non-linear prices , 2004, J. Econ. Theory.

[13]  Alan J. Hoffman,et al.  Systems of inequalities involving convex functions , 1957 .

[14]  Andreu Mas-Colell,et al.  A New Approach to the Existence of Equilibria in Vector Lattices , 1991 .

[15]  G. Debreu.  VALUATION EQUILIBRIUM AND PARETO OPTIMUM. , 1954, Proceedings of the National Academy of Sciences of the United States of America.

[16]  C. Aliprantis,et al.  Portfolio dominance and optimality in infinite security markets , 1998 .

[17]  Paulo Klinger Monteiro,et al.  Equilibrium without uniform conditions , 1989 .

[18]  Isaac Namioka,et al.  Partially Ordered Linear Topological Spaces , 1974 .

[19]  P. Laurent.  Approximation et optimisation , 1972 .

[20]  Paulo Monteiro,et al.  Mas-Colell Price Equilibrium Existence Theorem the Case of Smooth Disposal , 2000 .

[21]  V. Barbu,et al.  Convexity and optimization in banach spaces , 1972 .

[22]  M. Florenzano,et al.  Finite Dimensional Convexity and Optimization , 2001 .

[23]  Charalambos D. Aliprantis,et al.  Positive Operators , 2006 .

[24]  Rabee Tourky,et al.  A New Approach to the Limit Theorem on the Core of an Economy in Vector Lattices , 1998 .

[25]  Charalambos D. Aliprantis,et al.  Locally solid Riesz spaces , 1978 .

[26]  Nicholas C. Yannelis,et al.  EQUILIBRIA IN BANACH LATTICES WITHOUT ORDERED PREFERENCES , 1986 .

[27]  Monique Florenzano,et al.  Decentralizing Edgeworth equilibria in economies with many commodities , 1999 .

[28]  R. Tourky,et al.  The super order dual of an ordered vector space and the Riesz–Kantorovich formula , 2001 .

[29]  Kim C. Border,et al.  Infinite Dimensional Analysis: A Hitchhiker’s Guide , 1994 .

[30]  S. Semmes.  Topological Vector Spaces , 2003 .

[31]  Nizar Allouch,et al.  Edgeworth and Walras equilibria of an arbitrage-free exchange economy , 2000 .

[32]  M. Florenzano,et al.  Production equilibria in vector lattices , 2001 .

[33]  Andreu Mas-Colell,et al.  The Price Equilibrium Existence Problem in Topological Vector Lattice s , 1986 .

[34]  Konrad Podczeck,et al.  Equilibria in vector lattices without ordered preferences or uniform properness , 1996 .

[35]  Charalambos D. Aliprantis,et al.  Edgeworth equilibria in production economies , 1987 .