A Classical Search Game in Discrete Locations

Autor:	Clarkson, Jake, Lin, Kyle Y., Glazebrook, Kevin D.
Rok vydání:	2021
Předmět:	Statistics - Machine Learning Computer Science - Computer Science and Game Theory Computer Science - Machine Learning Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among $n$ discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at location $i$ takes $t_i$ time units and detects the hider -- if hidden there -- independently with probability $q_i$, for $i=1,\ldots,n$. The hider aims to maximize the expected time until detection, while the searcher aims to minimize it. We prove the existence of an optimal strategy for each player. In particular, the hider's optimal mixed strategy hides in each location with a nonzero probability, and the searcher's optimal mixed strategy can be constructed with up to $n$ simple search sequences. We develop an algorithm to compute an optimal strategy for each player, and compare the optimal hiding strategy with the simple hiding strategy which gives the searcher no location preference at the beginning of the search. Comment: 55 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2103.09310 Zobrazit plný text záznamu View this record from Arxiv