Gap-minimizing prices and quadratic core convergence (Q1100995)

We study the decentralization of core allocations by price vectors chosen, essentially, to minimize the competitive gap. In the setting of \textit{G. Debreu} [ibid. 2, 1-7 (1975; Zbl 0307.90007)] and \textit{B. Grodal} [J. Math. Econ. 2, 171-186 (1975; Zbl 0331.90018)], the competitive gap with respect to these gap-minimizing prices goes to zero as the inverse of the square of the number of agents; in Debreu's setting, the convergence is uniform over agents while in Grodal's setting, we show convergence on average.