Date of Award

2026

Document Type

Thesis

Degree Name

Bachelor of Science

Department

Mathematics

First Advisor

Dr. Jeremy Lecrone

Abstract

This thesis studies the pursuer evader surveillance game with a triangular obstacle in the short-term. In the game, the pursuer aims to maintain surveillance of the evader as long as possible while the evader aims to break surveillance in a finite time. We classify the player strategies into  ideal ones and best admissible ones. The outcome of the game is determined by line of sight. We reduce the 4D game to a 3D game with a boundary separating two different local regimes. When the evader starts inside the threshold, we show that there exists an admissible evader that maintains an upward motion for a small time interval to terminate the game. When the evader starts outside the threshold, we show that there exists an admissible pursuer who can force the evader to have a downward motion for a small time interval so that the game duration is strictly positive. These results provide a geometric interpretation of the game and clarify the local behaviors of the value function.

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