# Time-Dependent Surveillance-Evasion Games

## TL;DR

This paper introduces algorithms for time-dependent surveillance-evasion games where an evader minimizes exposure while a moving observer maximizes it, using advanced game theory and optimization techniques to find equilibrium strategies.

## Contribution

It develops efficient algorithms for Nash Equilibrium policies in time-dependent SE games, extending previous frameworks with new optimization and dynamic programming methods.

## Key findings

- Algorithms successfully compute equilibrium strategies in complex environments.
- The method handles various sensor types and obstacle configurations.
- Results demonstrate effective evasion and surveillance strategies.

## Abstract

Surveillance-Evasion (SE) games form an important class of adversarial trajectory-planning problems. We consider time-dependent SE games, in which an Evader is trying to reach its target while minimizing the cumulative exposure to a moving enemy Observer. That Observer is simultaneously aiming to maximize the same exposure by choosing how often to use each of its predefined patrol trajectories. Following the framework introduced in Gilles and Vladimirsky (arXiv:1812.10620), we develop efficient algorithms for finding Nash Equilibrium policies for both players by blending techniques from semi-infinite game theory, convex optimization, and multi-objective dynamic programming on continuous planning spaces. We illustrate our method on several examples with Observers using omnidirectional and angle-restricted sensors on a domain with occluding obstacles.