  We consider a cascade network where a sequence of nodes each send a message
to their downstream neighbor to enable coordination, the first node having
access to an information signal. An adversary also receives all of the
communication as well as additional side-information. The performance of the
system is measured by a payoff function evaluated on actions produced at each
of the nodes, including the adversary. The challenge is to effectively use a
secret key to infuse some level of privacy into the encoding, in order thwart
the adversary's attempt to reduce the payoff. We obtain information-theoretic
inner and outer bounds on performance, and give examples where they are tight.
From these bounds, we also derive the optimal equivocation for this setting as
a special case.
