Secrecy in cascade networks

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 the communication as well as additional side-information. The performance of the system is measured by a payoff function over all actions produced by the nodes as well as the adversary. The challenge is to maintain secrecy from the adversary in order thwart his attempt to reduce the payoff. We obtain inner and outer bounds on performance, and give examples where they are tight. From these bounds, we also derive the optimal equivocation that can be achieved in this setting, as a special case.