A Classical Search Game in Discrete Locations
This work addresses a theoretical problem in game theory and search optimization, providing foundational results for discrete search games, but it is incremental as it builds upon known models.
The paper tackles a two-person zero-sum search game where a hider hides among discrete locations and a searcher tries to find them, proving the existence of optimal strategies for both players and developing an algorithm to compute these strategies, with the hider's optimal strategy involving nonzero probabilities for each location and the searcher's using up to n simple sequences.
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.