A Game Model of Search and Pursuit

TL;DR

This paper extends a game theoretic model of search and pursuit by incorporating inspection times, total inspection constraints, and a repeated game setting where capture probabilities evolve based on past outcomes.

Contribution

It introduces modifications to the existing model by including inspection times, total inspection limits, and a dynamic repeated game framework with evolving capture probabilities.

Findings

Incorporating inspection times affects optimal search strategies.

Total inspection time constraints influence pursuit success.

Repeated interactions lead to updated perceptions of capture probabilities.

Abstract

Shmuel Gal and Jerome Casas have recently introduced a game theoretic model that combines search and pursuit by a predator for a prey animal. The prey (hider) can hide in a finite number of locations. The predator (searcher) can inspect any k of these locations. If the prey is not in any of these, the prey wins. If the prey is found at an inspected location, a pursuit begins which is successful for the predator with a known capture probability which depends on the location. We modify the problem so that each location takes a certain time to inspect and the predator has total inspection time k. We also consider a repeated game model where the capture probabilities only become known to the players over time, as each successful escape from a location lowers its perceived value capture probability.