Caching and Accumulation Games

In this paper, we investigate a discrete search game called the Multiple Caching Game where the searcher’s aim is to find all of a set of d treasures hidden in n locations. Allowed queries are sets of locations of size k, and the searcher wins if in all d queries, at least one treasure is hidden in one of the k picked locations. Pálvölgyi showed that the value of the game is at most (Formula presented) with equality for large enough n. We conjecture the exact cases of equality. We also investigate variants of the game and show an example where their values are different, answering a question of Pálvölgyi. This game is closely related to a continuous variant, Alpern’s Caching Game, based on which we define other continous variants of the multiple caching game and examine their values.