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The best rate of convergence of the core. (English) Zbl 0552.90014
It has been demonstrated by R. J. Aumann [Econometrica 43, 611-646 (1975; Zbl 0325.90082)] that the rate of convergence of the core can be arbitrarily slow unless some conditions are imposed on the limit economy. In the present paper an open set of limit economies is exhibited so that for each economy in the open set, a sequence of economies can be found converging to it with the rate of convergence of the core as slow as \(0(1/(n^{1/2+\epsilon})\) for any given \(\epsilon >0\). This means that it is impossible to impose generic conditions similar to the regularity conditions used by G. Debreu [J. Math. Econ. 2, 1-7 (1975; Zbl 0307.90007)] and B. Grodal [ibid. 2, 171-186 (1975; Zbl 0331.90018)] on the limit economy to obtain a rate of convergence better than \(0(1/n^{1/2})\).
Reviewer: W.Pauwels

91B50 General equilibrium theory
91A40 Other game-theoretic models
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