Given a k–sample model indexed by one real parameter θ,the statistician's task is considered to estimate θ robustly when Nature may assign varying contamination to each sample subject to some overall average contamination. After determining the estimators which are asymptotically optimum for a fixed contamination, asymptotic minimax estimators. least favorable contaminations, and saddle points are derived for the contamination game. Different loss criteria are employed: asymptotic variance, confidence interval loss, mean squared error, and general non–negative, monotone, convex loss. The different kinds of contamination used are: constant(symmetric)∈–contamination in the variance case, and for the other loss criteria infinitesimal contamination of the types: HELLINGER, total variation, ∈–contamination.Minimax estimators for infinitesimal contamination are obtained by uniformly bounding the influence curves(∈–contamination, total variation) or their variance (HELLINGER). The existence of saddle points is shown quite generally, only for infinitesimal ∈– contamination depending on a proporrionality property of the minimax influence curve. In all cases, the least favorable contamination assignt largest contamination to the most informative samples.