How to hide information for later use on networks

In an accumulation game a Hider secretly distributes his given total wealth h>1 among n locations while a Searcher picks r locations and confiscates the material placed there. The Hider wins if what is left at the remaining locations is at least 1 otherwise the Searcher wins. Accumulation games were originally introduced to study certain covert activities, but the game also relates to secret sharing and food caching. In this paper we introduce a network structure on the game, restricting the Searcher to pick locations that are near and show how this leads to combinatorial considerations.