  We consider the min-cost multicast problem (under network coding) with
multiple correlated sources where each terminal wants to losslessly reconstruct
all the sources. We study the inefficiency brought forth by the selfish
behavior of the terminals in this scenario by modeling it as a noncooperative
game among the terminals. The degradation in performance due to the lack of
regulation is measured by the {\it Price of Anarchy} (POA), which is defined as
the ratio between the cost of the worst possible \textit{Wardrop equilibrium}
and the socially optimum cost. Our main result is that in contrast with the
case of independent sources, the presence of source correlations can
significantly increase the price of anarchy. Towards establishing this result,
we first characterize the socially optimal flow and rate allocation in terms of
four intuitive conditions. Next, we show that the Wardrop equilibrium is a
socially optimal solution for a different set of (related) cost functions.
Using this, we construct explicit examples that demonstrate that the POA $> 1$
and determine near-tight upper bounds on the POA as well. The main techniques
in our analysis are Lagrangian duality theory and the usage of the
supermodularity of conditional entropy.
