  Interacting urns with exponential reinforcement were introduced and studied
in Launay (2011). As its parameter $\rho$ tends to $\iy$, this reinforcement
mechanism converges to the "generalized" reinforcement, in which the
probability of draw may be 0 or 1 for some of the colors, depending on the
current configuration. For a single urn, the generalized reinforcement is easy
to analyse. We introduce and study the generalized interacting urn model with
two or more urns and two colors. Our results concern the law of the so-called
non-conformist urns, and answer in the asymptotic sense one of the open
questions from the above mentioned paper.
