Hide-and-Seek with Directional Sensing

TL;DR

This paper introduces a novel search heuristic and a game-theoretic model for a hide-and-seek game involving directional sensing, analyzing the expected search cost and security levels through randomized sampling techniques.

Contribution

It presents a new heuristic for directional sensing search and models the game as a large-dimensional zero-sum game with probabilistic security guarantees using randomized sampling.

Findings

Heuristic achieves comparable cost to security level with few samples.

Increasing samples enhances probabilistic security.

Modeling provides bounds on search efficiency and security.

Abstract

We consider a game played between a hider, who hides a static object in one of several possible positions in a bounded planar region, and a searcher, who wishes to reach the object by querying sensors placed in the plane. The searcher is a mobile agent, and whenever it physically visits a sensor, the sensor returns a random direction, corresponding to a half-plane in which the hidden object is located. We first present a novel search heuristic and characterize bounds on the expected distance covered before reaching the object. Next, we model this game as a large-dimensional zero-sum dynamic game and we apply a recently introduced randomized sampling technique that provides a probabilistic level of security to the hider. We observe that, when the randomized sampling approach is only allowed to select a very small number of samples, the cost of the heuristic is comparable to the security level provided by the randomized procedure. However, as we allow the number of samples to increase, the randomized procedure provides a higher probabilistic security level.