The problem of finding iterative methods for computing economic equili
bria is a longstanding issue. Saari (1985) proved an impossibility res
ult, demonstrating that among a large class of mechanisms a universall
y convergent one does not exist. We generalize Saari's result by expan
ding the class of mechanisms and admit an universally convergent mecha
nism. The proof is constructive and employs results from the theory of
chaotic dynamical systems.