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 [Formula: see text] treasures hidden in [Formula: see text] locations. Allowed queries are sets of locations of size [Formula: see text], and the searcher wins if in all [Formula: see text] queries, at least one treasure is hidden in one of the [Formula: see text] picked locations. Pálvölgyi showed that the value of the game is at most [Formula: see text], with equality for large enough [Formula: see text]. 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.