Caching and Accumulation Games

à ron Jánosik, Csenge Miklós, Dániel G. Simon and Kristóf Zólomy
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à ron Jánosik: Department of Operations Research, Eötvös Loránd University, Budapest, Hungary
Csenge Miklós: ��Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark
Dániel G. Simon: ��Department of Computer Science, Eötvös Loránd University, Budapest, Hungary§HUN-REN Alfréd Rényi Institute of Mathematics, Budapest, Hungary
Kristóf Zólomy: ��Department of Computer Science, Eötvös Loránd University, Budapest, Hungary

International Game Theory Review (IGTR), 2025, vol. 27, issue 03, 1-25

Abstract: 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 kd n+d−1 d, 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.

Keywords: Search theory; multiple caching game (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0219198925500057

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