Searching for Multiple Objects in Multiple Locations
Thomas Lidbetter, Kyle Lin

TL;DR
This paper introduces new game-theoretic models for searching multiple hidden objects across various locations, providing full solutions for regret-based strategies and partial solutions for search cost scenarios.
Contribution
It formulates novel models for multi-object search problems, offering comprehensive solutions for the regret version and partial insights for the search cost version.
Findings
Full solution for the regret version of the game.
Partial solution for the search cost version.
Analysis of variations with at most one ball per box.
Abstract
Many practical search problems concern the search for multiple hidden objects or agents, such as earthquake survivors. In such problems, knowing only the list of possible locations, the Searcher needs to find all the hidden objects by visiting these locations one by one. To study this problem, we formulate new game-theoretic models of discrete search between a Hider and a Searcher. The Hider hides balls in boxes, and the Searcher opens the boxes one by one with the aim of finding all the balls. Every time the Searcher opens a box she must pay its search cost, and she either finds one of the balls it contains or learns that it is empty. If the Hider is an adversary, an appropriate payoff function may be the expected total search cost paid to find all the balls, while if the Hider is Nature, a more appropriate payoff function may be the difference between the total amount paid and…
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Taxonomy
TopicsOptimization and Search Problems · Advanced Bandit Algorithms Research · Auction Theory and Applications
