  Information is a key component in determining the price of an asset in
financial markets, and the main objective of this paper is to study the spread
of information in this context. The network of interactions in financial
markets is modeled using a Galton-Watson tree where vertices represent the
traders and where two traders are connected by an edge if one of the two
traders sells the asset to the other trader. The information starts from a
given vertex and spreads through the edges of the graph going independently
from seller to buyer with probability $p$ and from buyer to seller with
probability $q$. In particular, the set of traders who are aware of the
information is a (bidirectional) bond percolation cluster on the Galton-Watson
tree. Using some conditioning techniques and a partition of the cluster of open
edges into subtrees, we compute explicitly the first and second moments of the
cluster size, i.e., the random number of traders who learn about the
information. We also prove exponential decay of the diameter of the cluster in
the subcritical phase.
