Annals of Operations Research

, Volume 114, Issue 1–4, pp 229–243 | Cite as

Continuity Properties of Walras Equilibrium Points

  • Alejandro Jofré
  • Roger J.-B. Wets


We explore convergence notions for bivariate functions that yield convergence and stability results for their max/inf points. The results are then applied to obtain continuity results for Walras equilibrium points under perturbations of the utility functions of the agents.

market equilibrium lopsided convergence Ky Fan functions min/sup-points max/inf-points 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H. Attouch, Variational Convergence for Functions and Operators (Pitman, 1984).Google Scholar
  2. [2]
    H. Attouch and R.J.-B. Wets, Convergence des points min/sup et de points fixes, Comptes Rendus de l'Académie des Sciences de Paris 296 (1983) 657-660.Google Scholar
  3. [3]
    J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis (Wiley, 1984).Google Scholar
  4. [4]
    J.-P. Aubin and H. Frankowska, Set-Valued Analysis (Birkhäuser, 1990).Google Scholar
  5. [5]
    Y. Balasko, Fundations of the Theory of General Equilibrium (Academic Press, 1988).Google Scholar
  6. [6]
    Y. Balasko, Smooth equilibrium analysis with price dependent preferences, Preprint (2000).Google Scholar
  7. [7]
    J.M. Bonnisseau, Regular economies without ordered preferences, Preprint (2001).Google Scholar
  8. [8]
    S. Dafermos, Exchange price equilibria and variational inequalities, Mathematical Programming 46 (1990) 391-402.Google Scholar
  9. [9]
    G. Debreu, Theory of Value (Wiley, 1959).Google Scholar
  10. [10]
    K. Fan, A minimax inequality and applications, in: Inequalities, Vol. 3, ed. A. Shisha (Academic Press, 1972) pp. 103-113.Google Scholar
  11. [11]
    S. Flåm, On variational stability in competitive economies, Set-Valued Analysis 2 (1994) 159-173.Google Scholar
  12. [12]
    S. Flåm and B. Sandvik, Competitive equilibrium: Walras meets Darwin, Optimization 47 (2000) 137-153.Google Scholar
  13. [13]
    F. Hahn, Stability, in: Handbook of Mathematical Economics, eds. K. Arrow and M. Intriligator (North-Holland, 1981) chapter 16, pp. 745-793.Google Scholar
  14. [14]
    A. Jofre and R.J.-B.Wets, Continuity results for Nash and Walras equilibrium points (2002), in preparation.Google Scholar
  15. [15]
    R. Lucchetti and F. Patrone, Closure and uppersemicontinuity results in mathematical programming, Nash and economic equilibria, Optimization 17 (1986) 619-628.Google Scholar
  16. [16]
    A.Mas-Colell, The Theory of General Economic Equilibrium: A Differentiable Approach, Econometric Society Monographs (Cambridge University Press, 1985).Google Scholar
  17. [17]
    A. Mas-Colell, M. Whinston and J. Green, Microeconomic Theorem (Oxford University Press, 1995).Google Scholar
  18. [18]
    R.T. Rockafellar and R.J.-B.Wets, Variational Analysis (Springer, 1998).Google Scholar
  19. [19]
    S. Simons, The continuity of inf-sup with applications, Archiv der Mathematik 48 (1987) 426-437.Google Scholar
  20. [20]
    S. Simons, Minmax and Monotonicity, Lecture Notes in Mathematics, Vol. 1693 (Springer, 1998).Google Scholar
  21. [21]
    S. Smale, Global analysis and economics, IV: Finiteness and stability of equilibria with general consumption sets and production, Journal of Mathematical Economics 1(2) (1974) 119-127.Google Scholar
  22. [22]
    S. Smale, A convergent process of price adjustment and global newton methods, Journal of Mathematical Economics 3(2) (1976) 107-120.Google Scholar
  23. [23]
    S. Smale, Global analysis and economics, in: Handbook of Mathematical Economics, eds. K. Arrow and M. Intriligator (North-Holland, 1981) pp. 331-370.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Alejandro Jofré
    • 1
  • Roger J.-B. Wets
    • 2
  1. 1.Ingeneria MatematicaUniversidad de ChileSantiagoChile
  2. 2.Department of MathematicsUniversity of CaliforniaDavisUSA

Personalised recommendations