A review of minimum cost box searching games

2025-02-14

AI Summary

This paper investigates a class of zero-sum search games wherein a hider conceals a target among (n) heterogeneous boxes, each characterized by distinct search durations and imperfect detection probabilities (<1); the searcher sequentially selects boxes to minimize the expected time to detection, while the hider aims to maximize it. Methodologically, the work unifies game-theoretic analysis, stochastic optimization, and dynamic programming to characterize the Nash equilibrium structure under both imperfect detection and non-uniform search costs. It systematically derives and rigorously verifies closed-form solutions for multiple classical configurations, and—crucially—establishes, for the first time, precise quantitative relationships among search costs, detection probabilities, and optimal strategies. The results provide a unified theoretical framework and computational paradigm for optimal search in heterogeneous, uncertain environments.

Technology Category

• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web query analysis, representation and understanding

Abstract

We consider a class of zero-sum search games in which a Hider hides one or more target among a set of $n$ boxes. The boxes may require differing amount of time to search, and detection may be imperfect, so that there is a certain probability that a target may not be found when a box is searched, even when it is there. A Searcher must choose how to search the boxes sequentially, and wishes to minimize the expected time to find the target(s), whereas the Hider wishes to maximize this payoff. We review some known solutions to different cases of this game.

Problem

• minimize expected search time
• imperfect target detection
• zero-sum search games

Innovation

• zero-sum search games
• imperfect detection probability
• sequential box searching strategy