Geodesic
Parametric Stability of Solutions in Models of Economic Equilibrium
Journal of convex analysis, Tome 19 (2012) no. 4, pp. 975-997.

Voir la notice de l'article provenant de la source Heldermann Verlag

Recent results about strong metric regularity of solution mappings are applied to a challenging situation in basic mathematical economics, a model of market equilibrium in the exchange of goods. The solution mapping goes from the initial endowments of the agents to the goods they end up with and the supporting prices, and the issue is whether, relative to a particular equilibrium, it has a single-valued, Lipschitz continuous localization. A positive answer is obtained when the chosen goods are not too distant from the endowments. A counterexample is furnished to demonstrate that, when the distance is too great, such strong metric regularity can fail, with the equilibrium then being unstable with respect to tiny shifts in the endowment parameters, even bifurcating or, on the other hand, vanishing abruptly.
Classification : 49J53, 47J07, 49J40, 49K40, 90C31
Mots-clés : Strong metric regularity, solution stability, economic equilibrium, ample survivability, nonmonotone variational inequalities, convex analysis, variational analysis, Robinson's theorem 
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     author = {A. L. Dontchev and R. T. Rockafellar},
     title = {Parametric {Stability} of {Solutions} in {Models} of {Economic} {Equilibrium}},
     journal = {Journal of convex analysis},
     pages = {975--997},
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     volume = {19},
     number = {4},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_4_JCA_2012_19_4_a4/}
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A. L. Dontchev; R. T. Rockafellar. Parametric Stability of Solutions in Models of Economic Equilibrium. Journal of convex analysis, Tome 19 (2012) no. 4, pp. 975-997. http://geodesic.mathdoc.fr/item/JCA_2012_19_4_JCA_2012_19_4_a4/