  A major goal in Algorithmic Game Theory is to justify equilibrium concepts
from an algorithmic and complexity perspective. One appealing approach is to
identify robust natural distributed algorithms that converge quickly to an
equilibrium. This paper addresses a lack of robustness in existing convergence
results for discrete forms of tatonnement, including the fact that it need not
converge when buyers have linear utility functions. This work achieves greater
robustness by seeking approximate rather than exact convergence in large market
settings.
  More specifically, this paper shows that for Fisher markets with buyers
having CES utility functions, including linear utility functions, tatonnement
will converge quickly to an approximate equilibrium (i.e. at a linear rate),
modulo a suitable large market assumption. The quality of the approximation is
a function of the parameters of the large market assumption.
