Computing Optimal Strategies for a Search Game in Discrete Locations

TL;DR

This paper introduces an algorithm to compute optimal strategies in a two-player search game involving discrete locations, balancing search times and detection probabilities to maximize or minimize detection time.

Contribution

The paper presents a novel algorithm for finding optimal strategies in a search game with probabilistic detection and varying search times, supported by numerical analysis.

Findings

Efficient algorithm for computing optimal strategies.

Optimal hiding strategies depend on detection probabilities and search times.

Numerical results illustrate strategy characteristics.

Abstract

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 $\alpha_i$, for $i=1,\ldots,n$. The hider aims to maximize the expected time until detection, while the searcher aims to minimize it. We present an algorithm to compute an optimal strategy for each player. We demonstrate the algorithm's efficiency in a numerical study, in which we also study the characteristics of the optimal hiding strategy.