Abstract
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.
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References
H. Attouch, Variational Convergence for Functions and Operators (Pitman, 1984).
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.
J.-P. Aubin and I. Ekeland, Applied Nonlinear Analysis (Wiley, 1984).
J.-P. Aubin and H. Frankowska, Set-Valued Analysis (Birkhäuser, 1990).
Y. Balasko, Fundations of the Theory of General Equilibrium (Academic Press, 1988).
Y. Balasko, Smooth equilibrium analysis with price dependent preferences, Preprint (2000).
J.M. Bonnisseau, Regular economies without ordered preferences, Preprint (2001).
S. Dafermos, Exchange price equilibria and variational inequalities, Mathematical Programming 46 (1990) 391-402.
G. Debreu, Theory of Value (Wiley, 1959).
K. Fan, A minimax inequality and applications, in: Inequalities, Vol. 3, ed. A. Shisha (Academic Press, 1972) pp. 103-113.
S. Flåm, On variational stability in competitive economies, Set-Valued Analysis 2 (1994) 159-173.
S. Flåm and B. Sandvik, Competitive equilibrium: Walras meets Darwin, Optimization 47 (2000) 137-153.
F. Hahn, Stability, in: Handbook of Mathematical Economics, eds. K. Arrow and M. Intriligator (North-Holland, 1981) chapter 16, pp. 745-793.
A. Jofre and R.J.-B.Wets, Continuity results for Nash and Walras equilibrium points (2002), in preparation.
R. Lucchetti and F. Patrone, Closure and uppersemicontinuity results in mathematical programming, Nash and economic equilibria, Optimization 17 (1986) 619-628.
A.Mas-Colell, The Theory of General Economic Equilibrium: A Differentiable Approach, Econometric Society Monographs (Cambridge University Press, 1985).
A. Mas-Colell, M. Whinston and J. Green, Microeconomic Theorem (Oxford University Press, 1995).
R.T. Rockafellar and R.J.-B.Wets, Variational Analysis (Springer, 1998).
S. Simons, The continuity of inf-sup with applications, Archiv der Mathematik 48 (1987) 426-437.
S. Simons, Minmax and Monotonicity, Lecture Notes in Mathematics, Vol. 1693 (Springer, 1998).
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.
S. Smale, A convergent process of price adjustment and global newton methods, Journal of Mathematical Economics 3(2) (1976) 107-120.
S. Smale, Global analysis and economics, in: Handbook of Mathematical Economics, eds. K. Arrow and M. Intriligator (North-Holland, 1981) pp. 331-370.
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Jofré, A., Wets, R.JB. Continuity Properties of Walras Equilibrium Points. Annals of Operations Research 114, 229–243 (2002). https://doi.org/10.1023/A:1021022522035
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DOI: https://doi.org/10.1023/A:1021022522035